Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
312 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 113 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. #11762833 | C2 | semidirect |
| 3. C4×C4⋊Dic17 | C2 | semidirect |
| 4. #11762568 | C2 | semidirect |
| 7. C4×Q8×C17 | C4 | semidirect |
| 8. C4×Q8×C17 | C4 | semidirect |
| 11. C4×D4×C17 | C4 | semidirect |
| 12. C4×D4×C17 | C4 | semidirect |
| 61. Q8×C17 | C4⋊C4 | semidirect |
| 65. D4×C17 | C4⋊C4 | semidirect |
| 104. C4×C17 | #104 | semidirect |
| 123. C4×Q8 | Dic17 | semidirect |
| 124. C4×Q8 | Dic17 | semidirect |
| 127. C4×D4 | Dic17 | semidirect |
| 128. C4×D4 | Dic17 | semidirect |
| 139. C17 | #1806 | semidirect |
| 177. Q8 | C4⋊Dic17 | semidirect |
| 181. D4 | C4⋊Dic17 | semidirect |
| 220. C4 | #10587508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11762833 | 2 |
| C2×#10587508 | 2 |
| C4×C4⋊Dic17 | 2 |
| #11762568 | 2 |
| C4×#41×C17 | 2 |
| #1806 | 17 |