Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 73 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. #30681986 | C2 | semidirect |
| 5. #30681710 | C2 | semidirect |
| 6. #30681698 | C2 | semidirect |
| 7. C4×M16×C263 | C2 | semidirect |
| 16. #22554388 | C4 | semidirect |
| 17. #22554386 | C4 | semidirect |
| 95. C263 | #1932 | semidirect |
| 101. C4×M16 | D263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30681986 | 2 |
| #30681954 | 2 |
| C2×#22554398 | 2 |
| #30681920 | 2 |
| #30681710 | 2 |
| #30681698 | 2 |
| C4×M16×C263 | 2 |
| #1932 | 263 |