Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 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. #30682738 | C2 | semidirect |
| 2. C2×#22554498 | C2 | semidirect |
| 3. #30682507 | C2 | semidirect |
| 4. #30681954 | C2 | semidirect |
| 5. #30681944 | C2 | semidirect |
| 6. #30681911 | C2 | semidirect |
| 7. #344×C263 | C2 | semidirect |
| 41. C2×Dic526 | D4 | semidirect |
| 50. C2×D1052 | D4 | semidirect |
| 69. M16×C263 | D4 | semidirect |
| 71. C2×C8×C263 | D4 | semidirect |
| 142. C263 | #2008 | semidirect |
| 150. #344 | D263 | semidirect |
| 208. M16 | D1052 | semidirect |
| 210. C2×C8 | D1052 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30682738 | 2 |
| C2×#22554498 | 2 |
| #30682507 | 2 |
| #30681954 | 2 |
| #30681944 | 2 |
| #30681911 | 2 |
| #344×C263 | 2 |
| #2008 | 263 |