Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
348 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 121 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. #26041573 | C2 | semidirect |
| 3. #26041572 | C2 | semidirect |
| 6. #26041488 | C2 | semidirect |
| 7. #26041487 | C2 | semidirect |
| 70. C2×Dic181 | Q16 | semidirect |
| 102. C181 | #3249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041831 | 2 |
| #26041573 | 2 |
| #26041572 | 2 |
| #26041520 | 2 |
| #26041518 | 2 |
| #26041488 | 2 |
| #26041487 | 2 |
| C2×#19153745 | 2 |
| #467×C181 | 2 |
| #3249 | 181 |