Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#19153781 | C2 | semidirect |
| 3. #26041614 | C2 | semidirect |
| 4. #26041589 | C2 | semidirect |
| 5. #26041500 | C2 | semidirect |
| 6. #26041437 | C2 | semidirect |
| 8. #26041385 | C2 | semidirect |
| 9. #26041376 | C2 | semidirect |
| 10. #26041333 | C2 | semidirect |
| 131. C181 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041810 | 2 |
| C2×#19153781 | 2 |
| #26041614 | 2 |
| #26041589 | 2 |
| #26041500 | 2 |
| #26041437 | 2 |
| #26041417 | 2 |
| #26041385 | 2 |
| #26041376 | 2 |
| #26041333 | 2 |
| #481×C181 | 2 |
| #3117 | 181 |