Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
138 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 53 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. #11762612 | C2 | semidirect |
| 4. C4×#63214 | C2 | semidirect |
| 5. C17×#499 | C2 | semidirect |
| 47. #499 | D17 | semidirect |
| 64. C17 | #2242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763193 | 2 |
| #11762612 | 2 |
| #11762609 | 2 |
| C4×#63214 | 2 |
| C17×#499 | 2 |
| #2242 | 17 |