Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
174 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 79 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×#63214 | C2 | semidirect |
| 2. C2×C16×D17 | C2 | semidirect |
| 4. #11762627 | C2 | semidirect |
| 5. #11762588 | C2 | semidirect |
| 6. C16×Dic17 | C2 | semidirect |
| 7. C17×C22⋊C16 | C2 | semidirect |
| 39. #63214 | D4 | semidirect |
| 46. C22⋊D17 | C16 | semidirect |
| 60. C22×C17 | C2×C16 | semidirect |
| 64. C2×D17 | C2×C16 | semidirect |
| 70. Dic17 | C2×C16 | semidirect |
| 76. C22⋊C16 | D17 | semidirect |
| 96. C17 | D4×C16 | semidirect |
| 138. C22 | C16×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63214 | 2 |
| C2×C16×D17 | 2 |
| C8×C22⋊D17 | 2 |
| #11762627 | 2 |
| #11762588 | 2 |
| C16×Dic17 | 2 |
| C17×C22⋊C16 | 2 |
| D4×C16 | 17 |