Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
198 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 65 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. #26041027 | C2 | semidirect |
| 5. #26041027 | C2 | semidirect |
| 6. #26041025 | C2 | semidirect |
| 7. #332×C181 | C2 | semidirect |
| 85. C181 | #1554 | semidirect |
| 93. #332 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041834 | 2 |
| #26041335 | 2 |
| #26041331 | 2 |
| #26041027 | 2 |
| #26041025 | 2 |
| #332×C181 | 2 |
| #1554 | 181 |