Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
302 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 93 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. #26041322 | C2 | semidirect |
| 4. #26041148 | C2 | semidirect |
| 5. #26041048 | C2 | semidirect |
| 6. #26041038 | C2 | semidirect |
| 15. #19153743 | C4 | semidirect |
| 31. #15668433 | C2×C4 | semidirect |
| 38. C4×Dic181 | C2×C4 | semidirect |
| 69. Q8×C181 | C4⋊C4 | semidirect |
| 73. D4×C181 | C4⋊C4 | semidirect |
| 112. C181 | #1859 | semidirect |
| 175. Q8 | #15668428 | semidirect |
| 179. D4 | #15668428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041322 | 2 |
| C2×#19153743 | 2 |
| #26041280 | 2 |
| #26041148 | 2 |
| #26041048 | 2 |
| #26041038 | 2 |
| #520×C181 | 2 |
| #1859 | 181 |