Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
336 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 113 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. #11763211 | C2 | semidirect |
| 3. #11763149 | C2 | semidirect |
| 4. #11763143 | C2 | semidirect |
| 5. #11763116 | C2 | semidirect |
| 6. #11763064 | C2 | semidirect |
| 8. #11762850 | C2 | semidirect |
| 9. C4×Q16×C17 | C2 | semidirect |
| 99. C4×Q16 | D17 | semidirect |
| 131. C17 | #3352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763500 | 2 |
| #11763211 | 2 |
| #11763149 | 2 |
| #11763143 | 2 |
| #11763116 | 2 |
| #11763064 | 2 |
| #11762888 | 2 |
| #11762850 | 2 |
| C4×Q16×C17 | 2 |
| #3352 | 17 |