Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
| 3. C2×#22554395 | C2 | semidirect |
| 5. #30681844 | C2 | semidirect |
| 7. C2×C4×C8×C263 | C2 | semidirect |
| 12. C2×#16862365 | C4 | semidirect |
| 79. C2×C4×C263 | SD16 | semidirect |
| 87. C8×C263 | C22⋊C4 | semidirect |
| 112. C263 | #1968 | semidirect |
| 118. C2×C4×C8 | D263 | semidirect |
| 192. C2×C4 | #16862365 | semidirect |
| 200. C8 | (C2×D263)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16862365 | 2 |
| C2×#22554402 | 2 |
| C2×#22554395 | 2 |
| C2×#22554392 | 2 |
| #30681844 | 2 |
| #30681840 | 2 |
| C2×C4×C8×C263 | 2 |
| #1968 | 263 |