Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #26041827 | C2 | semidirect |
| 2. C4×#15668450 | C2 | semidirect |
| 3. #26041601 | C2 | semidirect |
| 4. #26041564 | C2 | semidirect |
| 5. #26041560 | C2 | semidirect |
| 6. #26041471 | C2 | semidirect |
| 7. #26041423 | C2 | semidirect |
| 8. #26041388 | C2 | semidirect |
| 9. #26041380 | C2 | semidirect |
| 10. #26041335 | C2 | semidirect |
| 11. #460×C181 | C2 | semidirect |
| 88. D724 | #41 | semidirect |
| 106. Q8×C181 | #41 | semidirect |
| 144. C181 | #3115 | semidirect |
| 151. #460 | D181 | semidirect |
| 233. Q8 | #15668448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041827 | 2 |
| C4×#15668450 | 2 |
| #26041601 | 2 |
| #26041564 | 2 |
| #26041560 | 2 |
| #26041471 | 2 |
| #26041423 | 2 |
| #26041388 | 2 |
| #26041380 | 2 |
| #26041335 | 2 |
| #460×C181 | 2 |
| #3115 | 181 |