Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
418 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11763479 | C2 | semidirect |
| 3. #11763197 | C2 | semidirect |
| 4. #11763022 | C2 | semidirect |
| 5. #11763006 | C2 | semidirect |
| 6. #11763002 | C2 | semidirect |
| 7. #11763001 | C2 | semidirect |
| 8. #11762939 | C2 | semidirect |
| 9. #11762921 | C2 | semidirect |
| 10. C4×#63219 | C2 | semidirect |
| 11. C17×#493 | C2 | semidirect |
| 107. C8×C17 | #41 | semidirect |
| 132. #493 | D17 | semidirect |
| 175. C17 | #3399 | semidirect |
| 243. C8 | #63254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763545 | 2 |
| #11763479 | 2 |
| #11763197 | 2 |
| #11763022 | 2 |
| #11763006 | 2 |
| #11763002 | 2 |
| #11763001 | 2 |
| #11762939 | 2 |
| #11762921 | 2 |
| C4×#63219 | 2 |
| C17×#493 | 2 |
| #3399 | 17 |