Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
384 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 1. #11763545 | C2 | semidirect |
| 2. #11763474 | C2 | semidirect |
| 3. #11763167 | C2 | semidirect |
| 4. #11763097 | C2 | semidirect |
| 5. #11763091 | C2 | semidirect |
| 6. #11763023 | C2 | semidirect |
| 8. #11762939 | C2 | semidirect |
| 9. #11762918 | C2 | semidirect |
| 10. C4×#63219 | C2 | semidirect |
| 11. C17×#486 | C2 | semidirect |
| 123. #486 | D17 | semidirect |
| 165. C17 | #3373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763545 | 2 |
| #11763474 | 2 |
| #11763167 | 2 |
| #11763097 | 2 |
| #11763091 | 2 |
| #11763023 | 2 |
| #11763001 | 2 |
| #11762939 | 2 |
| #11762918 | 2 |
| C4×#63219 | 2 |
| C17×#486 | 2 |
| #3373 | 17 |