Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
552 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 153 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×#22576193 | C2 | semidirect |
| 2. C2×#22576191 | C2 | semidirect |
| 3. C2×#22576190 | C2 | semidirect |
| 5. C2×#22576158 | C2 | semidirect |
| 6. #31774290 | C2 | semidirect |
| 7. #31774288 | C2 | semidirect |
| 8. #31774275 | C2 | semidirect |
| 9. #31774268 | C2 | semidirect |
| 10. M16×Dic271 | C2 | semidirect |
| 11. C2×#137×C271 | C2 | semidirect |
| 62. #16864638 | D4 | semidirect |
| 86. M16×C271 | D4 | semidirect |
| 140. Dic271 | #137 | semidirect |
| 146. C271 | #3152 | semidirect |
| 151. C2×#137 | D271 | semidirect |
| 224. M16 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576193 | 2 |
| C2×#22576191 | 2 |
| C2×#22576190 | 2 |
| #31774443 | 2 |
| C2×#22576158 | 2 |
| #31774290 | 2 |
| #31774288 | 2 |
| #31774275 | 2 |
| #31774268 | 2 |
| M16×Dic271 | 2 |
| C2×#137×C271 | 2 |
| #3152 | 271 |