Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
402 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#22554390 | C2 | semidirect |
| 3. C2×#22554390 | C2 | semidirect |
| 4. #30681693 | C2 | semidirect |
| 5. #389×C263 | C2 | semidirect |
| 42. C4⋊C4×C263 | D4 | semidirect |
| 103. C263 | #2041 | semidirect |
| 108. #389 | D263 | semidirect |
| 146. C4⋊C4 | D1052 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22554467 | 2 |
| C2×#22554390 | 2 |
| #30681693 | 2 |
| #389×C263 | 2 |
| #2041 | 263 |