Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
460 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 127 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×Q16×D181 | C2 | semidirect |
| 4. #26041536 | C2 | semidirect |
| 5. #26041535 | C2 | semidirect |
| 6. #26041521 | C2 | semidirect |
| 7. #26041520 | C2 | semidirect |
| 8. #26041517 | C2 | semidirect |
| 9. #26041316 | C2 | semidirect |
| 10. #26041286 | C2 | semidirect |
| 11. #467×C181 | C2 | semidirect |
| 137. C181 | #3059 | semidirect |
| 147. #467 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D181 | 2 |
| C2×#19153822 | 2 |
| #26041852 | 2 |
| #26041536 | 2 |
| #26041535 | 2 |
| #26041521 | 2 |
| #26041520 | 2 |
| #26041517 | 2 |
| #26041316 | 2 |
| #26041286 | 2 |
| #467×C181 | 2 |
| #3059 | 181 |