Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
182 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 67 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. #11762888 | C2 | semidirect |
| 3. C8×D68 | C2 | semidirect |
| 4. #11762562 | C2 | semidirect |
| 5. #11762538 | C2 | semidirect |
| 6. #11762538 | C2 | semidirect |
| 7. C17×#322 | C2 | semidirect |
| 52. D68 | M16 | semidirect |
| 61. C8×C17 | D8 | semidirect |
| 85. #322 | D17 | semidirect |
| 106. C17 | #1581 | semidirect |
| 147. C8 | D136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D136 | 2 |
| #11762888 | 2 |
| C8×D68 | 2 |
| #11762562 | 2 |
| #11762538 | 2 |
| C17×#322 | 2 |
| #1581 | 17 |