Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
800 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 197 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×#22576158 | C2 | semidirect |
| 3. #31773817 | C2 | semidirect |
| 4. #31773802 | C2 | semidirect |
| 36. C22⋊Dic271 | Q8 | semidirect |
| 58. C2×Dic271 | C2×Q8 | semidirect |
| 77. C22×C271 | C4⋊Q8 | semidirect |
| 93. C271 | #2434 | semidirect |
| 171. C22 | #22576158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic542 | 2 |
| C2×#22576158 | 2 |
| #31773817 | 2 |
| #31773802 | 2 |
| #31773769 | 2 |
| C4×C22⋊Dic271 | 2 |
| C2×C22⋊Q8×C271 | 2 |
| #2434 | 271 |