Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 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. C22×Dic68 | C2 | semidirect |
| 2. C2×Q16×D17 | C2 | semidirect |
| 4. #11763187 | C2 | semidirect |
| 5. #11763051 | C2 | semidirect |
| 6. #11763018 | C2 | semidirect |
| 7. #11762966 | C2 | semidirect |
| 8. #11762964 | C2 | semidirect |
| 9. #11762903 | C2 | semidirect |
| 11. C17×#467 | C2 | semidirect |
| 78. Dic68 | D4 | semidirect |
| 90. C22⋊D17 | Q16 | semidirect |
| 113. C22×C17 | C2×Q16 | semidirect |
| 117. C2×D17 | C2×Q16 | semidirect |
| 127. Dic17 | C2×Q16 | semidirect |
| 133. #467 | D17 | semidirect |
| 173. C17 | D4×Q16 | semidirect |
| 248. C22 | Q16×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic68 | 2 |
| C2×Q16×D17 | 2 |
| #11763472 | 2 |
| #11763187 | 2 |
| #11763051 | 2 |
| #11763018 | 2 |
| #11762966 | 2 |
| #11762964 | 2 |
| #11762903 | 2 |
| C8×C22⋊D17 | 2 |
| C17×#467 | 2 |
| D4×Q16 | 17 |