Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
316 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 83 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×#19153751 | C2 | semidirect |
| 3. #26041283 | C2 | semidirect |
| 4. C2×#19153733 | C2 | semidirect |
| 5. C2×#19153732 | C2 | semidirect |
| 6. #26041235 | C2 | semidirect |
| 7. #418×C181 | C2 | semidirect |
| 12. C2×#15668434 | C4 | semidirect |
| 111. C181 | #1978 | semidirect |
| 116. #418 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668434 | 2 |
| C2×#19153751 | 2 |
| #26041283 | 2 |
| C2×#19153733 | 2 |
| C2×#19153732 | 2 |
| #26041235 | 2 |
| #418×C181 | 2 |
| #1978 | 181 |