Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
376 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 143 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. #26041588 | C2 | semidirect |
| 4. #26041584 | C2 | semidirect |
| 5. #26041572 | C2 | semidirect |
| 6. #26041562 | C2 | semidirect |
| 72. C2×Q8×C181 | Q8 | semidirect |
| 129. C181 | #3078 | semidirect |
| 177. C2×Q8 | Dic362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041832 | 2 |
| C2×Q8×Dic181 | 2 |
| #26041588 | 2 |
| #26041584 | 2 |
| #26041572 | 2 |
| #26041562 | 2 |
| #26041322 | 2 |
| #26041321 | 2 |
| #26041302 | 2 |
| #26041288 | 2 |
| #419×C181 | 2 |
| #3078 | 181 |