Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 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. #23752908 | C2 | semidirect |
| 2. #23752614 | C2 | semidirect |
| 3. #23752537 | C2 | semidirect |
| 4. #23752526 | C2 | semidirect |
| 5. #23752513 | C2 | semidirect |
| 6. #23752465 | C2 | semidirect |
| 7. C4×D1208 | C2 | semidirect |
| 8. #23752254 | C2 | semidirect |
| 9. #436×C151 | C2 | semidirect |
| 102. C151 | #3355 | semidirect |
| 111. #436 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752908 | 2 |
| #23752614 | 2 |
| #23752537 | 2 |
| #23752526 | 2 |
| #23752513 | 2 |
| #23752465 | 2 |
| C4×D1208 | 2 |
| #23752254 | 2 |
| #436×C151 | 2 |
| #3355 | 151 |