Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
454 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 119 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. #23752743 | C2 | semidirect |
| 2. C2×#18012701 | C2 | semidirect |
| 3. #23752547 | C2 | semidirect |
| 4. #23752511 | C2 | semidirect |
| 5. #23752426 | C2 | semidirect |
| 6. #23752365 | C2 | semidirect |
| 8. #23752299 | C2 | semidirect |
| 9. #23752292 | C2 | semidirect |
| 10. #23752262 | C2 | semidirect |
| 11. #481×C151 | C2 | semidirect |
| 17. #18012730 | C22 | semidirect |
| 18. #18012726 | C22 | semidirect |
| 21. #18012704 | C22 | semidirect |
| 23. D4×Dic151 | C22 | semidirect |
| 31. #18012672 | C22 | semidirect |
| 32. Dic151⋊C8 | C22 | semidirect |
| 33. #18012662 | C22 | semidirect |
| 37. C8×Dic151 | C22 | semidirect |
| 40. #106×C151 | C22 | semidirect |
| 41. #102×C151 | C22 | semidirect |
| 140. C151 | #3105 | semidirect |
| 145. #481 | D151 | semidirect |
| 175. #106 | C2×D151 | semidirect |
| 180. #102 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752743 | 2 |
| C2×#18012701 | 2 |
| #23752547 | 2 |
| #23752511 | 2 |
| #23752426 | 2 |
| #23752365 | 2 |
| #23752345 | 2 |
| #23752299 | 2 |
| #23752292 | 2 |
| #23752262 | 2 |
| #481×C151 | 2 |
| #3105 | 151 |