Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
144 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 144 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 |
|---|---|---|
| 2. #26042208 | C2 | semidirect |
| 3. #26042207 | C2 | semidirect |
| 52. D181 | #368 | semidirect |
| 53. C181 | C2×#368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D181⋊#108 | 2 |
| #26042208 | 2 |
| #26042207 | 2 |
| C2×C16×D181 | 2 |
| C2×#368 | 181 |