Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
388 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 141 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. #11763142 | C2 | semidirect |
| 4. #11763104 | C2 | semidirect |
| 5. #11763048 | C2 | semidirect |
| 6. #11763016 | C2 | semidirect |
| 7. #11762965 | C2 | semidirect |
| 8. C4×#63231 | C2 | semidirect |
| 10. C2×#10587506 | C2 | semidirect |
| 82. D4×C17 | Q16 | semidirect |
| 163. C17 | #3299 | semidirect |
| 208. D4 | #63231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763516 | 2 |
| #11763159 | 2 |
| #11763142 | 2 |
| #11763104 | 2 |
| #11763048 | 2 |
| #11763016 | 2 |
| #11762965 | 2 |
| C4×#63231 | 2 |
| D4×#3622 | 2 |
| C2×#10587506 | 2 |
| D4×Q8×C17 | 2 |
| #3299 | 17 |