Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
402 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 4. #11762716 | C2 | semidirect |
| 5. #11762571 | C2 | semidirect |
| 6. #11762563 | C2 | semidirect |
| 7. C2×C17×#103 | C2 | semidirect |
| 15. C2×#63230 | C4 | semidirect |
| 32. C2×Q8×C17 | C2×C4 | semidirect |
| 61. C2×#3622 | C2×C4 | semidirect |
| 94. C2×Dic17 | SD16 | semidirect |
| 128. C2×#103 | D17 | semidirect |
| 159. C17 | #1877 | semidirect |
| 166. C2×Q8 | C4×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63230 | 2 |
| C2×#10587579 | 2 |
| C2×#10587492 | 2 |
| #11762716 | 2 |
| #11762571 | 2 |
| #11762563 | 2 |
| C2×C17×#103 | 2 |
| #1877 | 17 |