Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
166 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 166 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. #26041486 | C2 | semidirect |
| 3. C8×Dic362 | C2 | semidirect |
| 4. #26041032 | C2 | semidirect |
| 5. #26041025 | C2 | semidirect |
| 78. C181 | #1682 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041486 | 2 |
| #26041476 | 2 |
| C8×Dic362 | 2 |
| #26041032 | 2 |
| #26041025 | 2 |
| #26041023 | 2 |
| #486×C181 | 2 |
| #1682 | 181 |