Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
260 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 73 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. #11762831 | C2 | semidirect |
| 3. C4⋊C8×D17 | C2 | semidirect |
| 4. #11762556 | C2 | semidirect |
| 5. #11762554 | C2 | semidirect |
| 6. #11762553 | C2 | semidirect |
| 7. C17×#331 | C2 | semidirect |
| 100. #331 | D17 | semidirect |
| 123. C17 | #1547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763357 | 2 |
| #11762831 | 2 |
| C4⋊C8×D17 | 2 |
| #11762556 | 2 |
| #11762554 | 2 |
| #11762553 | 2 |
| C17×#331 | 2 |
| #1547 | 17 |