Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
336 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26041303 | C2 | semidirect |
| 4. #26041047 | C2 | semidirect |
| 5. #423×C181 | C2 | semidirect |
| 91. C4×C181 | #100 | semidirect |
| 103. C181 | #1800 | semidirect |
| 107. #423 | D181 | semidirect |
| 196. C4 | #19153732 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D724 | 2 |
| #26041303 | 2 |
| C2×#19153732 | 2 |
| #26041047 | 2 |
| #423×C181 | 2 |
| #1800 | 181 |