Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
264 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 264 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×#22554402 | C2 | semidirect |
| 4. #30681706 | C2 | semidirect |
| 5. C2×#108×C263 | C2 | semidirect |
| 8. #22554476 | C4 | semidirect |
| 84. C263 | #1815 | semidirect |
| 87. C2×#108 | D263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22554476 | 2 |
| C2×#22554402 | 2 |
| #30681940 | 2 |
| #30681706 | 2 |
| C2×#108×C263 | 2 |
| #1815 | 263 |