Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
440 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 131 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. #23752767 | C2 | semidirect |
| 3. #23752511 | C2 | semidirect |
| 4. #23752510 | C2 | semidirect |
| 5. #23752499 | C2 | semidirect |
| 6. #23752493 | C2 | semidirect |
| 7. #23752492 | C2 | semidirect |
| 8. #23752251 | C2 | semidirect |
| 9. #23752234 | C2 | semidirect |
| 11. #476×C151 | C2 | semidirect |
| 15. #18012739 | C22 | semidirect |
| 16. #18012730 | C22 | semidirect |
| 30. #18012673 | C22 | semidirect |
| 31. #18012672 | C22 | semidirect |
| 32. #18012670 | C22 | semidirect |
| 33. C4⋊(C151⋊C8) | C22 | semidirect |
| 34. Dic151⋊C8 | C22 | semidirect |
| 38. C4⋊Q8×C151 | C22 | semidirect |
| 40. #106×C151 | C22 | semidirect |
| 41. C4⋊C8×C151 | C22 | semidirect |
| 48. D4×D151 | Q8 | semidirect |
| 144. C151 | #3077 | semidirect |
| 151. #476 | D151 | semidirect |
| 161. C4⋊Q8 | C2×D151 | semidirect |
| 180. #106 | C2×D151 | semidirect |
| 183. C4⋊C8 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752767 | 2 |
| C4×D4×D151 | 2 |
| #23752511 | 2 |
| #23752510 | 2 |
| #23752499 | 2 |
| #23752493 | 2 |
| #23752492 | 2 |
| #23752251 | 2 |
| #23752234 | 2 |
| #23752215 | 2 |
| #476×C151 | 2 |
| #3077 | 151 |