Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
380 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 129 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. #26041646 | C2 | semidirect |
| 4. #26041628 | C2 | semidirect |
| 100. C181 | #3139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041832 | 2 |
| C2×#19153814 | 2 |
| #26041646 | 2 |
| #26041628 | 2 |
| #26041289 | 2 |
| #26041288 | 2 |
| #26041287 | 2 |
| M16×Dic181 | 2 |
| #419×C181 | 2 |
| #3139 | 181 |