Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
198 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 198 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. #26041655 | C2 | semidirect |
| 2. #26041474 | C2 | semidirect |
| 3. #26041357 | C2 | semidirect |
| 4. #26041029 | C2 | semidirect |
| 5. #26041023 | C2 | semidirect |
| 6. #26041022 | C2 | semidirect |
| 7. #459×C181 | C2 | semidirect |
| 53. #13089678 | D8 | semidirect |
| 92. C181 | #1687 | semidirect |
| 96. #459 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041655 | 2 |
| #26041474 | 2 |
| #26041357 | 2 |
| #26041029 | 2 |
| #26041023 | 2 |
| #26041022 | 2 |
| #459×C181 | 2 |
| #1687 | 181 |