Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
476 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 129 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. C2×#22576192 | C2 | semidirect |
| 2. #31774559 | C2 | semidirect |
| 3. #31774281 | C2 | semidirect |
| 4. #31774144 | C2 | semidirect |
| 5. #31774119 | C2 | semidirect |
| 6. #31774054 | C2 | semidirect |
| 7. #31774045 | C2 | semidirect |
| 8. #31773976 | C2 | semidirect |
| 9. C4×Q16×C271 | C2 | semidirect |
| 64. Q16×C271 | D4 | semidirect |
| 117. C271 | #3277 | semidirect |
| 126. C4×Q16 | D271 | semidirect |
| 170. Q16 | D1084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576192 | 2 |
| #31774559 | 2 |
| #31774281 | 2 |
| #31774144 | 2 |
| #31774119 | 2 |
| #31774054 | 2 |
| #31774045 | 2 |
| #31773976 | 2 |
| C4×Q16×C271 | 2 |
| #3277 | 271 |