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×#19153847 | C2 | semidirect |
| 3. #26041653 | C2 | semidirect |
| 4. #26041527 | C2 | semidirect |
| 5. #26041486 | C2 | semidirect |
| 6. #26041479 | C2 | semidirect |
| 7. #26041439 | C2 | semidirect |
| 8. #26041418 | C2 | semidirect |
| 9. C4×#15668439 | C2 | semidirect |
| 10. #26041357 | C2 | semidirect |
| 11. D4×Q8×C181 | C2 | semidirect |
| 52. #15668439 | D4 | semidirect |
| 126. C4×C181 | #137 | semidirect |
| 136. C181 | #3278 | semidirect |
| 140. D4×Q8 | D181 | semidirect |
| 265. C4 | #19153847 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153847 | 2 |
| #26041950 | 2 |
| #26041653 | 2 |
| #26041527 | 2 |
| #26041486 | 2 |
| #26041479 | 2 |
| #26041439 | 2 |
| #26041418 | 2 |
| C4×#15668439 | 2 |
| #26041357 | 2 |
| D4×Q8×C181 | 2 |
| #3278 | 181 |