Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
276 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 67 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. #26041307 | C2 | semidirect |
| 3. #26041289 | C2 | semidirect |
| 5. C2×#19153734 | C2 | semidirect |
| 6. #26041043 | C2 | semidirect |
| 100. C181 | #2046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668437 | 2 |
| #26041307 | 2 |
| #26041289 | 2 |
| #26041284 | 2 |
| C2×#19153734 | 2 |
| #26041043 | 2 |
| C2×#100×C181 | 2 |
| #2046 | 181 |