Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
176 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 64 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. #26042328 | C2 | semidirect |
| 3. #26042143 | C2 | semidirect |
| 4. #26042129 | C2 | semidirect |
| 6. #26042120 | C2 | semidirect |
| 31. #15668437 | C8 | semidirect |
| 47. Dic362 | C2×C8 | semidirect |
| 54. #13089678 | C2×C8 | semidirect |
| 77. C181 | SD16⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042328 | 2 |
| D4×#13089685 | 2 |
| #26042143 | 2 |
| #26042129 | 2 |
| D4⋊#13089685 | 2 |
| #26042120 | 2 |
| #26041370 | 2 |
| SD16⋊C8 | 181 |