Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
484 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#19153845 | C2 | semidirect |
| 3. C4×Q8×D181 | C2 | semidirect |
| 4. #26041500 | C2 | semidirect |
| 5. #26041499 | C2 | semidirect |
| 6. #26041490 | C2 | semidirect |
| 7. #26041489 | C2 | semidirect |
| 8. #26041476 | C2 | semidirect |
| 9. #26041301 | C2 | semidirect |
| 10. #26041277 | C2 | semidirect |
| 11. #460×C181 | C2 | semidirect |
| 50. Q8×D181 | D4 | semidirect |
| 132. C4×C181 | #137 | semidirect |
| 146. C181 | #3037 | semidirect |
| 156. #460 | D181 | semidirect |
| 285. C4 | #19153845 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153845 | 2 |
| #26041827 | 2 |
| C4×Q8×D181 | 2 |
| #26041500 | 2 |
| #26041499 | 2 |
| #26041490 | 2 |
| #26041489 | 2 |
| #26041476 | 2 |
| #26041301 | 2 |
| #26041277 | 2 |
| #460×C181 | 2 |
| #3037 | 181 |