Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
286 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 83 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. #23752254 | C2 | semidirect |
| 5. #23752077 | C2 | semidirect |
| 6. #23751973 | C2 | semidirect |
| 7. #343×C151 | C2 | semidirect |
| 19. #18012665 | C4 | semidirect |
| 47. C4×Dic151 | C2×C4 | semidirect |
| 53. M16×C151 | C2×C4 | semidirect |
| 111. C151 | #1860 | semidirect |
| 118. #343 | D151 | semidirect |
| 154. M16 | C4×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752693 | 2 |
| #23752254 | 2 |
| C2×#18012665 | 2 |
| #23752214 | 2 |
| #23752077 | 2 |
| #23751973 | 2 |
| #343×C151 | 2 |
| #1860 | 151 |