Finite Group DatabasebetaFinite Group DatabasebetaOrder 17728.
250 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 95 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 | C22⋊Q8×C277 | C2 |
| hypercenter | C22⋊Q8 | D277 |
| hypocenter | C277 | #538 |
| LCS | G ▷ C22×C277 ▷ C277 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22579875 | C2 | semidirect |
| 2. #22579869 | C2 | semidirect |
| 3. #22579865 | C2 | semidirect |
| 4. #22579855 | C2 | semidirect |
| 5. #22579854 | C2 | semidirect |
| 6. #22579850 | C2 | semidirect |
| 7. #22579840 | C2 | semidirect |
| 8. C2×#17984540 | C2 | semidirect |
| 9. C22⋊Q8×C277 | C2 | semidirect |
| 13. C2×D1108 | C22 | semidirect |
| 16. C2×C4×D277 | C22 | semidirect |
| 17. C4⋊Dic277 | C22 | semidirect |
| 18. #17984542 | C22 | semidirect |
| 23. #17984540 | C22 | semidirect |
| 24. #17984540 | C22 | semidirect |
| 25. C4×Dic277 | C22 | semidirect |
| 26. C2×Q8×C277 | C22 | semidirect |
| 28. C4⋊C4×C277 | C22 | semidirect |
| 29. C4⋊C4×C277 | C22 | semidirect |
| 74. C277 | #538 | semidirect |
| 79. C22⋊Q8 | D277 | semidirect |
| 86. C2×Q8 | C2×D277 | semidirect |
| 96. C4⋊C4 | C2×D277 | semidirect |
| 97. C4⋊C4 | C2×D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22579875 | 2 |
| #22579869 | 2 |
| #22579865 | 2 |
| #22579855 | 2 |
| #22579854 | 2 |
| #22579850 | 2 |
| #22579840 | 2 |
| C2×#17984540 | 2 |
| C22⋊Q8×C277 | 2 |
| #538 | 277 |