Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 324 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. #23752255 | C2 | semidirect |
| 3. #23752254 | C2 | semidirect |
| 6. #23751972 | C2 | semidirect |
| 7. #339×C151 | C2 | semidirect |
| 22. #18012655 | C4 | semidirect |
| 37. #14558988 | C2×C4 | semidirect |
| 51. M16×C151 | C2×C4 | semidirect |
| 114. C151 | #1856 | semidirect |
| 122. #339 | D151 | semidirect |
| 156. M16 | C4×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752686 | 2 |
| #23752255 | 2 |
| #23752254 | 2 |
| C2×#18012655 | 2 |
| #23752114 | 2 |
| #23751972 | 2 |
| #339×C151 | 2 |
| #1856 | 151 |