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×#19153848 | C2 | semidirect |
| 3. Q8×D724 | C2 | semidirect |
| 4. #26041652 | C2 | semidirect |
| 5. #26041526 | C2 | semidirect |
| 6. #26041489 | C2 | semidirect |
| 7. #26041479 | C2 | semidirect |
| 8. #26041444 | C2 | semidirect |
| 9. #26041419 | C2 | semidirect |
| 10. #26041358 | C2 | semidirect |
| 11. C4×Q16×C181 | C2 | semidirect |
| 72. Q16×C181 | D4 | semidirect |
| 126. C4×C181 | #137 | semidirect |
| 136. C181 | #3278 | semidirect |
| 147. C4×Q16 | D181 | semidirect |
| 197. Q16 | D724 | semidirect |
| 265. C4 | #19153848 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153848 | 2 |
| #26041951 | 2 |
| Q8×D724 | 2 |
| #26041652 | 2 |
| #26041526 | 2 |
| #26041489 | 2 |
| #26041479 | 2 |
| #26041444 | 2 |
| #26041419 | 2 |
| #26041358 | 2 |
| C4×Q16×C181 | 2 |
| #3278 | 181 |