Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
362 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 2. #26041586 | C2 | semidirect |
| 3. #26041586 | C2 | semidirect |
| 4. #26041574 | C2 | semidirect |
| 5. #26041564 | C2 | semidirect |
| 59. C2×Q8×C181 | Q8 | semidirect |
| 116. C181 | #3082 | semidirect |
| 161. C2×Q8 | Dic362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041907 | 2 |
| #26041586 | 2 |
| #26041574 | 2 |
| #26041564 | 2 |
| #26041322 | 2 |
| #26041315 | 2 |
| #26041306 | 2 |
| #26041288 | 2 |
| C2×#19153740 | 2 |
| #519×C181 | 2 |
| #3082 | 181 |