Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
424 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 133 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. #31774210 | C2 | semidirect |
| 3. #31774192 | C2 | semidirect |
| 4. #31774097 | C2 | semidirect |
| 5. #31774036 | C2 | semidirect |
| 6. #31773995 | C2 | semidirect |
| 7. #31773954 | C2 | semidirect |
| 8. C2×C4×Q8×C271 | C2 | semidirect |
| 76. Q8×C271 | #41 | semidirect |
| 111. C271 | #3112 | semidirect |
| 114. C2×C4×Q8 | D271 | semidirect |
| 181. Q8 | #16864654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774447 | 2 |
| #31774210 | 2 |
| #31774192 | 2 |
| #31774097 | 2 |
| #31774036 | 2 |
| #31773995 | 2 |
| #31773954 | 2 |
| C2×C4×Q8×C271 | 2 |
| #3112 | 271 |