Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
360 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 85 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. C2×#19153745 | C2 | semidirect |
| 3. C2×#19153736 | C2 | semidirect |
| 4. #26041180 | C2 | semidirect |
| 5. #340×C181 | C2 | semidirect |
| 54. C2×Dic181 | D8 | semidirect |
| 89. C181 | #2054 | semidirect |
| 95. #340 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1448 | 2 |
| C2×#19153745 | 2 |
| C2×#19153736 | 2 |
| #26041180 | 2 |
| #340×C181 | 2 |
| #2054 | 181 |