Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 65 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. #30682334 | C2 | semidirect |
| 2. #30682223 | C2 | semidirect |
| 4. #30681684 | C2 | semidirect |
| 5. Q8⋊(C263⋊C8) | C2 | semidirect |
| 61. Q8×C263 | SD16 | semidirect |
| 92. C263 | #1651 | semidirect |
| 150. Q8 | #16862364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30682334 | 2 |
| #30682223 | 2 |
| #30682143 | 2 |
| #30681684 | 2 |
| Q8⋊(C263⋊C8) | 2 |
| D4⋊(C263⋊C8) | 2 |
| D4×Q8×C263 | 2 |
| #1651 | 263 |