Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
384 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 173 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. #26041337 | C2 | semidirect |
| 3. #26041333 | C2 | semidirect |
| 4. #26041307 | C2 | semidirect |
| 5. #26041305 | C2 | semidirect |
| 7. M16×Dic181 | C2 | semidirect |
| 8. C2×#19153726 | C2 | semidirect |
| 93. C181 | #2923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×Dic181 | 2 |
| #26041337 | 2 |
| #26041333 | 2 |
| #26041307 | 2 |
| #26041305 | 2 |
| #26041246 | 2 |
| M16×Dic181 | 2 |
| C2×#19153726 | 2 |
| #408×C181 | 2 |
| #2923 | 181 |