Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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×#10587574 | C2 | semidirect |
| 3. #11763103 | C2 | semidirect |
| 4. #11763098 | C2 | semidirect |
| 5. #11763093 | C2 | semidirect |
| 6. #11763088 | C2 | semidirect |
| 7. #11762852 | C2 | semidirect |
| 8. #11762832 | C2 | semidirect |
| 11. C17×#428 | C2 | semidirect |
| 50. #63252 | Q8 | semidirect |
| 104. D68 | C2×Q8 | semidirect |
| 111. Dic34 | C2×Q8 | semidirect |
| 141. #428 | D17 | semidirect |
| 181. C17 | #3079 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587574 | 2 |
| #11763277 | 2 |
| #11763103 | 2 |
| #11763098 | 2 |
| #11763093 | 2 |
| #11763088 | 2 |
| #11762852 | 2 |
| #11762832 | 2 |
| #11762811 | 2 |
| #11762808 | 2 |
| C17×#428 | 2 |
| #3079 | 17 |