Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
278 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 278 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. #26041951 | C2 | semidirect |
| 2. #26041655 | C2 | semidirect |
| 3. #26041471 | C2 | semidirect |
| 4. #26041022 | C2 | semidirect |
| 5. Q8⋊#13089678 | C2 | semidirect |
| 6. #26041006 | C2 | semidirect |
| 7. #460×C181 | C2 | semidirect |
| 71. Q8×C181 | D8 | semidirect |
| 107. C181 | #1621 | semidirect |
| 111. #460 | D181 | semidirect |
| 164. Q8 | #15668434 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041951 | 2 |
| #26041655 | 2 |
| #26041471 | 2 |
| #26041022 | 2 |
| Q8⋊#13089678 | 2 |
| #26041006 | 2 |
| #460×C181 | 2 |
| #1621 | 181 |