Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 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. #26041907 | C2 | semidirect |
| 3. #26041587 | C2 | semidirect |
| 4. #26041580 | C2 | semidirect |
| 5. #26041570 | C2 | semidirect |
| 6. #26041565 | C2 | semidirect |
| 7. #26041321 | C2 | semidirect |
| 8. C2×#19153748 | C2 | semidirect |
| 11. #424×C181 | C2 | semidirect |
| 42. #15668449 | Q8 | semidirect |
| 123. C181 | #3084 | semidirect |
| 133. #424 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041907 | 2 |
| #26041759 | 2 |
| #26041587 | 2 |
| #26041580 | 2 |
| #26041570 | 2 |
| #26041565 | 2 |
| #26041321 | 2 |
| C2×#19153748 | 2 |
| #26041281 | 2 |
| #26041276 | 2 |
| #424×C181 | 2 |
| #3084 | 181 |