Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 57 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. D8×Dic17 | C2 | semidirect |
| 3. #11762891 | C2 | semidirect |
| 4. #11762636 | C2 | semidirect |
| 5. #11762611 | C2 | semidirect |
| 6. #11762584 | C2 | semidirect |
| 7. C17×#357 | C2 | semidirect |
| 15. #10587497 | C4 | semidirect |
| 25. D8×C17 | C2×C4 | semidirect |
| 34. D136 | C2×C4 | semidirect |
| 36. #63214 | C2×C4 | semidirect |
| 72. #357 | D17 | semidirect |
| 91. C17 | #2177 | semidirect |
| 99. D8 | C4×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587497 | 2 |
| D8×Dic17 | 2 |
| #11762891 | 2 |
| #11762636 | 2 |
| #11762611 | 2 |
| #11762584 | 2 |
| C17×#357 | 2 |
| #2177 | 17 |