Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
482 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 482 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×#19153839 | C2 | semidirect |
| 2. #26041940 | C2 | semidirect |
| 3. #26041664 | C2 | semidirect |
| 4. #26041517 | C2 | semidirect |
| 5. #26041515 | C2 | semidirect |
| 6. #26041503 | C2 | semidirect |
| 7. #26041440 | C2 | semidirect |
| 8. #26041418 | C2 | semidirect |
| 9. Q16×Dic181 | C2 | semidirect |
| 10. C8×C22⋊D181 | C2 | semidirect |
| 11. C22×Q16×C181 | C2 | semidirect |
| 76. Q16×C181 | D4 | semidirect |
| 113. C22×C181 | #135 | semidirect |
| 136. C181 | #3285 | semidirect |
| 139. C22×Q16 | D181 | semidirect |
| 195. Q16 | C22⋊D181 | semidirect |
| 256. C22 | #19153839 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153839 | 2 |
| #26041940 | 2 |
| #26041664 | 2 |
| #26041517 | 2 |
| #26041515 | 2 |
| #26041503 | 2 |
| #26041440 | 2 |
| #26041418 | 2 |
| Q16×Dic181 | 2 |
| C8×C22⋊D181 | 2 |
| C22×Q16×C181 | 2 |
| #3285 | 181 |