Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
488 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23752763 | C2 | semidirect |
| 2. C4×D4×D151 | C2 | semidirect |
| 3. #23752532 | C2 | semidirect |
| 4. #23752499 | C2 | semidirect |
| 5. #23752408 | C2 | semidirect |
| 6. #23752407 | C2 | semidirect |
| 7. #23752347 | C2 | semidirect |
| 8. #23752323 | C2 | semidirect |
| 9. #23752321 | C2 | semidirect |
| 10. #23752268 | C2 | semidirect |
| 11. #476×C151 | C2 | semidirect |
| 17. #18012736 | C22 | semidirect |
| 25. #18012701 | C22 | semidirect |
| 31. #18012670 | C22 | semidirect |
| 32. C4⋊(C151⋊C8) | C22 | semidirect |
| 33. #18012661 | C22 | semidirect |
| 35. #18012659 | C22 | semidirect |
| 37. #18012649 | C22 | semidirect |
| 38. C4⋊Q8×C151 | C22 | semidirect |
| 40. #106×C151 | C22 | semidirect |
| 41. C4⋊C8×C151 | C22 | semidirect |
| 96. D604 | #41 | semidirect |
| 115. D4×C151 | #41 | semidirect |
| 154. C151 | #3109 | semidirect |
| 160. #476 | D151 | semidirect |
| 172. C4⋊Q8 | C2×D151 | semidirect |
| 189. #106 | C2×D151 | semidirect |
| 191. C4⋊C8 | C2×D151 | semidirect |
| 256. D4 | #14559005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752763 | 2 |
| C4×D4×D151 | 2 |
| #23752532 | 2 |
| #23752499 | 2 |
| #23752408 | 2 |
| #23752407 | 2 |
| #23752347 | 2 |
| #23752323 | 2 |
| #23752321 | 2 |
| #23752268 | 2 |
| #476×C151 | 2 |
| #3109 | 151 |