Finite Group DatabasebetaFinite Group DatabasebetaOrder 1216.
334 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 107 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×D19 |
| commutator, socle, cosocle | C22×C19 | C24 |
| Fitting | C4×D4×C19 | C2 |
| hypercenter | C4×D4 | D19 |
| hypocenter | C19 | #546 |
| LCS | G ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#64541 | C2 | semidirect |
| 2. C22×D76 | C2 | semidirect |
| 3. C4×D4×C19 | C2 | semidirect |
| 4. #10597383 | C2 | semidirect |
| 5. #10597376 | C2 | semidirect |
| 6. #10597370 | C2 | semidirect |
| 7. #10597340 | C2 | semidirect |
| 8. #10597330 | C2 | semidirect |
| 9. C22⋊C4×D19 | C2 | semidirect |
| 10. #10597321 | C2 | semidirect |
| 11. C4×D76 | C2 | semidirect |
| 15. C22×C4×C19 | C22 | semidirect |
| 16. C2×C22⋊D19 | C22 | semidirect |
| 17. C2×C22⋊D19 | C22 | semidirect |
| 23. C2×C4×D19 | C22 | semidirect |
| 24. C2×C4×D19 | C22 | semidirect |
| 25. C2×Dic38 | C22 | semidirect |
| 26. C4⋊C4×C19 | C22 | semidirect |
| 28. C22⋊C4×C19 | C22 | semidirect |
| 29. C42×C19 | C22 | semidirect |
| 31. (C2×D19)⋊C4 | C22 | semidirect |
| 32. (C2×D19)⋊C4 | C22 | semidirect |
| 33. (C2×D19)⋊C4 | C22 | semidirect |
| 34. (C2×D19)⋊C4 | C22 | semidirect |
| 35. C4⋊Dic19 | C22 | semidirect |
| 36. Dic19⋊C4 | C22 | semidirect |
| 58. D76 | D4 | semidirect |
| 67. C22×C19 | #41 | semidirect |
| 100. C4×D4 | D19 | semidirect |
| 102. C19 | #546 | semidirect |
| 116. C22×C4 | C2×D19 | semidirect |
| 119. C4⋊C4 | C2×D19 | semidirect |
| 126. C22⋊C4 | C2×D19 | semidirect |
| 127. C42 | C2×D19 | semidirect |
| 165. C22 | #64541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64541 | 2 |
| C22×D76 | 2 |
| C4×D4×C19 | 2 |
| #10597383 | 2 |
| #10597376 | 2 |
| #10597370 | 2 |
| #10597340 | 2 |
| #10597330 | 2 |
| C22⋊C4×D19 | 2 |
| #10597321 | 2 |
| C4×D76 | 2 |
| #546 | 19 |