Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
236 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 1. #26041986 | C2 | semidirect |
| 2. #26041652 | C2 | semidirect |
| 3. #26041480 | C2 | semidirect |
| 5. #26041027 | C2 | semidirect |
| 6. #26041011 | C2 | semidirect |
| 7. D4⋊C8×C181 | C2 | semidirect |
| 66. D4×C181 | SD16 | semidirect |
| 96. C181 | #1622 | semidirect |
| 104. D4⋊C8 | D181 | semidirect |
| 158. D4 | #15668438 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041986 | 2 |
| #26041652 | 2 |
| #26041480 | 2 |
| #26041474 | 2 |
| #26041027 | 2 |
| #26041011 | 2 |
| D4⋊C8×C181 | 2 |
| #1622 | 181 |