Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11763545 | C2 | semidirect |
| 2. #11763192 | C2 | semidirect |
| 3. #11763022 | C2 | semidirect |
| 4. #11763006 | C2 | semidirect |
| 5. C8×Dic34 | C2 | semidirect |
| 6. C4×Dic68 | C2 | semidirect |
| 7. D8×Dic17 | C2 | semidirect |
| 114. C17 | #3396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763545 | 2 |
| #11763192 | 2 |
| #11763022 | 2 |
| #11763006 | 2 |
| C8×Dic34 | 2 |
| C4×Dic68 | 2 |
| D8×Dic17 | 2 |
| C17×#493 | 2 |
| #3396 | 17 |