Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
224 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 3. #13089685⋊C8 | C2 | semidirect |
| 4. C8×#13089685 | C2 | semidirect |
| 19. #15668458 | C8 | direct (N × H) |
| 36. #13089685 | C2×C8 | semidirect |
| 44. #13089678 | M16 | semidirect |
| 51. C8×C181 | M16 | semidirect |
| 67. C181 | C8×M16 | semidirect |
| 119. C8 | #15668458 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042296 | 2 |
| C4×#15668458 | 2 |
| #13089685⋊C8 | 2 |
| C8×#13089685 | 2 |
| C2×C8×Dic181 | 2 |
| C8×M16 | 181 |