Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
164 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 49 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×#10587499 | C2 | semidirect |
| 2. C2×C16×D17 | C2 | semidirect |
| 3. #11763047 | C2 | semidirect |
| 5. #11762636 | C2 | semidirect |
| 6. #11762611 | C2 | semidirect |
| 7. C17×#358 | C2 | semidirect |
| 39. #63214 | D4 | semidirect |
| 64. C2×D17 | SD32 | semidirect |
| 76. #358 | D17 | semidirect |
| 96. C17 | #2217 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587499 | 2 |
| C2×C16×D17 | 2 |
| #11763047 | 2 |
| #11763046 | 2 |
| #11762636 | 2 |
| #11762611 | 2 |
| C17×#358 | 2 |
| #2217 | 17 |