Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
334 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 334 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 |
|---|---|---|
| 4. #26041289 | C2 | semidirect |
| 5. #26041184 | C2 | semidirect |
| 6. #26041040 | C2 | semidirect |
| 7. #343×C181 | C2 | semidirect |
| 11. #19153849 | C4 | semidirect |
| 37. C2×Dic362 | C2×C4 | semidirect |
| 61. M16×C181 | C2×C4 | semidirect |
| 124. C181 | #1882 | semidirect |
| 131. #343 | D181 | semidirect |
| 177. M16 | C4×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153849 | 2 |
| #26041760 | 2 |
| C2×#19153742 | 2 |
| #26041289 | 2 |
| #26041184 | 2 |
| #26041040 | 2 |
| #343×C181 | 2 |
| #1882 | 181 |