Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
402 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 133 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. #11763366 | C2 | semidirect |
| 3. #11763214 | C2 | semidirect |
| 4. #11763182 | C2 | semidirect |
| 5. #11763160 | C2 | semidirect |
| 6. #11763156 | C2 | semidirect |
| 7. #11763055 | C2 | semidirect |
| 8. #11762911 | C2 | semidirect |
| 9. C4×M16×C17 | C2 | semidirect |
| 90. C8×C17 | #41 | semidirect |
| 116. C4×M16 | D17 | semidirect |
| 147. C17 | #3182 | semidirect |
| 203. C8 | #63252 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763366 | 2 |
| #11763359 | 2 |
| #11763214 | 2 |
| #11763182 | 2 |
| #11763160 | 2 |
| #11763156 | 2 |
| #11763055 | 2 |
| #11762911 | 2 |
| C4×M16×C17 | 2 |
| #3182 | 17 |