Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
314 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 157 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. #26041409 | C2 | semidirect |
| 3. #26041408 | C2 | semidirect |
| 4. #26041407 | C2 | semidirect |
| 5. #26041406 | C2 | semidirect |
| 91. C181 | #2987 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041832 | 2 |
| #26041409 | 2 |
| #26041408 | 2 |
| #26041407 | 2 |
| #26041406 | 2 |
| #26041340 | 2 |
| #26041337 | 2 |
| #26041333 | 2 |
| #433×C181 | 2 |
| #2987 | 181 |