Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
176 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 53 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. #26041626 | C2 | semidirect |
| 2. #26041484 | C2 | semidirect |
| 4. #26041030 | C2 | semidirect |
| 5. #26041024 | C2 | semidirect |
| 6. #26041022 | C2 | semidirect |
| 7. #436×C181 | C2 | semidirect |
| 84. C181 | #1701 | semidirect |
| 89. #436 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041626 | 2 |
| #26041484 | 2 |
| #26041474 | 2 |
| #26041030 | 2 |
| #26041024 | 2 |
| #26041022 | 2 |
| #436×C181 | 2 |
| #1701 | 181 |