Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
276 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 86 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. #26042295 | C2 | semidirect |
| 2. C2×C4×#13089685 | C2 | semidirect |
| 3. #26042129 | C2 | semidirect |
| 4. #26042127 | C2 | semidirect |
| 27. #15668449 | C8 | semidirect |
| 55. Dic362 | C2×C8 | semidirect |
| 57. D724 | C2×C8 | semidirect |
| 98. C181 | #1476 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042295 | 2 |
| C2×C4×#13089685 | 2 |
| #26042129 | 2 |
| #26042127 | 2 |
| #26041747 | 2 |
| #1476 | 181 |