Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11763159 | C2 | semidirect |
| 3. #11763147 | C2 | semidirect |
| 4. #11763104 | C2 | semidirect |
| 5. #11763057 | C2 | semidirect |
| 6. #11763011 | C2 | semidirect |
| 7. #11762948 | C2 | semidirect |
| 8. C4×#63230 | C2 | semidirect |
| 9. #11762887 | C2 | semidirect |
| 10. #11762818 | C2 | semidirect |
| 11. D4×Q8×C17 | C2 | semidirect |
| 123. D4×Q8 | D17 | semidirect |
| 167. C17 | #3329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763524 | 2 |
| #11763159 | 2 |
| #11763147 | 2 |
| #11763104 | 2 |
| #11763057 | 2 |
| #11763011 | 2 |
| #11762948 | 2 |
| C4×#63230 | 2 |
| #11762887 | 2 |
| #11762818 | 2 |
| D4×Q8×C17 | 2 |
| #3329 | 17 |