Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26042094 | C2 | semidirect |
| 2. #26042093 | C2 | semidirect |
| 3. #26041657 | C2 | semidirect |
| 4. #26041554 | C2 | semidirect |
| 5. #26041552 | C2 | semidirect |
| 6. #26041551 | C2 | semidirect |
| 7. #26041462 | C2 | semidirect |
| 8. #26041460 | C2 | semidirect |
| 9. #26041396 | C2 | semidirect |
| 10. #26041394 | C2 | semidirect |
| 11. #578×C181 | C2 | semidirect |
| 146. C181 | #3293 | semidirect |
| 150. #578 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042094 | 2 |
| #26042093 | 2 |
| #26041657 | 2 |
| #26041554 | 2 |
| #26041552 | 2 |
| #26041551 | 2 |
| #26041462 | 2 |
| #26041460 | 2 |
| #26041396 | 2 |
| #26041394 | 2 |
| #578×C181 | 2 |
| #3293 | 181 |