Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
438 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 107 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×D4×Dic17 | C2 | semidirect |
| 3. C2×#10587492 | C2 | semidirect |
| 4. #11762710 | C2 | semidirect |
| 5. #11762571 | C2 | semidirect |
| 6. #11762563 | C2 | semidirect |
| 7. C2×C17×#102 | C2 | semidirect |
| 18. C2×#63228 | C4 | semidirect |
| 47. C2×D68 | C2×C4 | semidirect |
| 63. C2×#3622 | C2×C4 | semidirect |
| 82. D4×C17 | C22⋊C4 | semidirect |
| 101. C2×Dic17 | D8 | semidirect |
| 141. C2×#102 | D17 | semidirect |
| 172. C17 | #1879 | semidirect |
| 233. D4 | #63227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63228 | 2 |
| C2×D4×Dic17 | 2 |
| C2×#10587492 | 2 |
| #11762710 | 2 |
| #11762571 | 2 |
| #11762563 | 2 |
| C2×C17×#102 | 2 |
| #1879 | 17 |