Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
332 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 2. #30681995 | C2 | semidirect |
| 3. #30681681 | C2 | semidirect |
| 4. #432×C263 | C2 | semidirect |
| 12. C4⋊(C263⋊C8) | C22 | semidirect |
| 16. C4⋊C8×C263 | C22 | semidirect |
| 79. C263 | #1555 | semidirect |
| 83. #432 | D263 | semidirect |
| 94. C4⋊C8 | C2×D263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22554467 | 2 |
| #30681995 | 2 |
| #30681681 | 2 |
| #432×C263 | 2 |
| #1555 | 263 |