Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
496 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 135 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. C2×#18012769 | C2 | semidirect |
| 2. C2×M16×D151 | C2 | semidirect |
| 4. C2×#18012719 | C2 | semidirect |
| 5. #23752469 | C2 | semidirect |
| 6. #23752457 | C2 | semidirect |
| 7. #23752452 | C2 | semidirect |
| 8. #23752440 | C2 | semidirect |
| 9. #23752252 | C2 | semidirect |
| 10. #23752222 | C2 | semidirect |
| 11. #417×C151 | C2 | semidirect |
| 15. C2×#14558994 | C22 | semidirect |
| 16. C2×#14558992 | C22 | semidirect |
| 36. #18012672 | C22 | semidirect |
| 37. #18012670 | C22 | semidirect |
| 38. #18012664 | C22 | semidirect |
| 39. #18012664 | C22 | semidirect |
| 43. #103×C151 | C22 | semidirect |
| 44. #102×C151 | C22 | semidirect |
| 62. #14558988 | D4 | semidirect |
| 145. C2×D151 | #137 | semidirect |
| 163. C151 | #3056 | semidirect |
| 175. #417 | D151 | semidirect |
| 207. #103 | C2×D151 | semidirect |
| 208. #102 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012769 | 2 |
| C2×M16×D151 | 2 |
| #23752719 | 2 |
| C2×#18012719 | 2 |
| #23752469 | 2 |
| #23752457 | 2 |
| #23752452 | 2 |
| #23752440 | 2 |
| #23752252 | 2 |
| #23752222 | 2 |
| #417×C151 | 2 |
| #3056 | 151 |