Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#19153838 | C2 | semidirect |
| 2. #26041950 | C2 | semidirect |
| 3. #26041656 | C2 | semidirect |
| 4. #26041515 | C2 | semidirect |
| 5. #26041480 | C2 | semidirect |
| 6. #26041426 | C2 | semidirect |
| 7. C4×Dic724 | C2 | semidirect |
| 8. C8×D4×C181 | C2 | semidirect |
| 38. Dic724 | D4 | semidirect |
| 87. C4×C181 | #135 | semidirect |
| 97. C181 | #3287 | semidirect |
| 106. C8×D4 | D181 | semidirect |
| 187. C4 | #19153838 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153838 | 2 |
| #26041950 | 2 |
| #26041656 | 2 |
| #26041515 | 2 |
| #26041480 | 2 |
| #26041426 | 2 |
| C4×Dic724 | 2 |
| C8×D4×C181 | 2 |
| #3287 | 181 |