Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
414 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. C2×#18012715 | C2 | semidirect |
| 3. #23752551 | C2 | semidirect |
| 4. #23752545 | C2 | semidirect |
| 5. #23752531 | C2 | semidirect |
| 6. #23752467 | C2 | semidirect |
| 7. #23752461 | C2 | semidirect |
| 8. #23752373 | C2 | semidirect |
| 9. #23752351 | C2 | semidirect |
| 10. #23752174 | C2 | semidirect |
| 11. #451×C151 | C2 | semidirect |
| 14. C2×#14558991 | C22 | semidirect |
| 31. #18012672 | C22 | semidirect |
| 32. #18012671 | C22 | semidirect |
| 33. #18012663 | C22 | semidirect |
| 34. #18012663 | C22 | semidirect |
| 35. #18012661 | C22 | semidirect |
| 39. C2×Q16×C151 | C22 | semidirect |
| 41. #103×C151 | C22 | semidirect |
| 149. C151 | #3196 | semidirect |
| 159. #451 | D151 | semidirect |
| 165. C2×Q16 | C2×D151 | semidirect |
| 188. #103 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752725 | 2 |
| C2×#18012715 | 2 |
| #23752551 | 2 |
| #23752545 | 2 |
| #23752531 | 2 |
| #23752467 | 2 |
| #23752461 | 2 |
| #23752373 | 2 |
| #23752351 | 2 |
| #23752174 | 2 |
| #451×C151 | 2 |
| #3196 | 151 |