Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
278 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 57 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. #30682610 | C2 | semidirect |
| 2. #30682314 | C2 | semidirect |
| 3. #30682130 | C2 | semidirect |
| 4. #30681681 | C2 | semidirect |
| 5. Q8⋊(C263⋊C8) | C2 | semidirect |
| 6. #30681665 | C2 | semidirect |
| 7. #460×C263 | C2 | semidirect |
| 71. Q8×C263 | D8 | semidirect |
| 107. C263 | #1621 | semidirect |
| 111. #460 | D263 | semidirect |
| 164. Q8 | #16862361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30682610 | 2 |
| #30682314 | 2 |
| #30682130 | 2 |
| #30681681 | 2 |
| Q8⋊(C263⋊C8) | 2 |
| #30681665 | 2 |
| #460×C263 | 2 |
| #1621 | 263 |