Finite Group DatabasebetaFinite Group DatabasebetaOrder 17728.
334 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D277 |
| commutator, socle, cosocle | C22×C277 | C24 |
| Fitting | C4×D4×C277 | C2 |
| hypercenter | C4×D4 | D277 |
| hypocenter | C277 | #546 |
| LCS | G ▷ C22×C277 ▷ C277 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#17984562 | C2 | semidirect |
| 2. C2×D4×D277 | C2 | semidirect |
| 3. #22579868 | C2 | semidirect |
| 4. #22579864 | C2 | semidirect |
| 5. #22579860 | C2 | semidirect |
| 6. #22579855 | C2 | semidirect |
| 7. #22579854 | C2 | semidirect |
| 8. #22579850 | C2 | semidirect |
| 9. C4×D1108 | C2 | semidirect |
| 10. C2×#17984540 | C2 | semidirect |
| 11. C4×D4×C277 | C2 | semidirect |
| 14. C2×Dic554 | C22 | semidirect |
| 17. C2×D1108 | C22 | semidirect |
| 19. C2×C22⋊D277 | C22 | semidirect |
| 21. C22×Dic277 | C22 | semidirect |
| 23. C2×C4×D277 | C22 | semidirect |
| 24. C4⋊Dic277 | C22 | semidirect |
| 25. C4⋊Dic277 | C22 | semidirect |
| 28. #17984540 | C22 | semidirect |
| 29. #17984540 | C22 | semidirect |
| 30. #17984540 | C22 | semidirect |
| 31. #17984540 | C22 | semidirect |
| 33. C22×C4×C277 | C22 | semidirect |
| 34. C4⋊C4×C277 | C22 | semidirect |
| 35. C22⋊C4×C277 | C22 | semidirect |
| 36. C42×C277 | C22 | semidirect |
| 56. D4×C277 | D4 | semidirect |
| 75. C2×D277 | #41 | semidirect |
| 90. C277 | #546 | semidirect |
| 101. C4×D4 | D277 | semidirect |
| 116. C22×C4 | C2×D277 | semidirect |
| 119. C4⋊C4 | C2×D277 | semidirect |
| 126. C22⋊C4 | C2×D277 | semidirect |
| 127. C42 | C2×D277 | semidirect |
| 141. D4 | D1108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984562 | 2 |
| C2×D4×D277 | 2 |
| #22579868 | 2 |
| #22579864 | 2 |
| #22579860 | 2 |
| #22579855 | 2 |
| #22579854 | 2 |
| #22579850 | 2 |
| C4×D1108 | 2 |
| C2×#17984540 | 2 |
| C4×D4×C277 | 2 |
| #546 | 277 |