Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
266 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 57 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×D136 | C2 | semidirect |
| 2. C2×D272 | C2 | semidirect |
| 3. #11763045 | C2 | semidirect |
| 4. #11762611 | C2 | semidirect |
| 5. C17×C22⋊C16 | C2 | semidirect |
| 12. C2×D136 | C22 | semidirect |
| 13. C2×C16×C17 | C22 | semidirect |
| 15. #10587489 | C22 | semidirect |
| 33. D136 | D4 | semidirect |
| 57. C22×C17 | D16 | semidirect |
| 74. C22⋊C16 | D17 | semidirect |
| 89. C2×C16 | C2×D17 | semidirect |
| 92. C17 | #2184 | semidirect |
| 139. C22 | D272 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D136 | 2 |
| C2×D272 | 2 |
| #11763045 | 2 |
| #11762611 | 2 |
| C17×C22⋊C16 | 2 |
| #2184 | 17 |