Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 133 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. #26041762 | C2 | semidirect |
| 3. #26041621 | C2 | semidirect |
| 4. #26041615 | C2 | semidirect |
| 5. #26041604 | C2 | semidirect |
| 6. #26041593 | C2 | semidirect |
| 7. #26041321 | C2 | semidirect |
| 8. C2×#19153750 | C2 | semidirect |
| 9. #26041281 | C2 | semidirect |
| 10. #26041276 | C2 | semidirect |
| 11. #408×C181 | C2 | semidirect |
| 133. C181 | #3098 | semidirect |
| 145. #408 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041857 | 2 |
| #26041762 | 2 |
| #26041621 | 2 |
| #26041615 | 2 |
| #26041604 | 2 |
| #26041593 | 2 |
| #26041321 | 2 |
| C2×#19153750 | 2 |
| #26041281 | 2 |
| #26041276 | 2 |
| #408×C181 | 2 |
| #3098 | 181 |