Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
164 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 71 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. C2×C16×D17 | C2 | semidirect |
| 3. #11762627 | C2 | semidirect |
| 4. C22⋊#63214 | C2 | semidirect |
| 5. #11762588 | C2 | semidirect |
| 6. #11762584 | C2 | semidirect |
| 7. C2×C17×M32 | C2 | semidirect |
| 37. C16×C17 | D4 | semidirect |
| 64. C2×D17 | M32 | semidirect |
| 71. C2×M32 | D17 | semidirect |
| 96. C17 | #2168 | semidirect |
| 115. C16 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C16×D17 | 2 |
| C8×C22⋊D17 | 2 |
| #11762627 | 2 |
| C22⋊#63214 | 2 |
| #11762588 | 2 |
| #11762584 | 2 |
| C2×C17×M32 | 2 |
| #2168 | 17 |