Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
174 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 50 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. D8×#595 | C2 | semidirect |
| 2. #11763735 | C2 | semidirect |
| 3. #11763721 | C2 | semidirect |
| 4. C16×#595 | C2 | semidirect |
| 12. C17×D16 | C4 | semidirect |
| 13. #10587497 | C4 | semidirect |
| 14. D272 | C4 | semidirect |
| 22. D8×C17 | C2×C4 | semidirect |
| 24. D136 | C2×C4 | semidirect |
| 27. C16×C17 | C2×C4 | semidirect |
| 28. #63214 | C2×C4 | semidirect |
| 49. #595 | D16 | direct (N × H) |
| 66. D16 | #595 | direct (N × H) |
| 72. C17 | C4×D16 | semidirect |
| 77. D8 | C2×#595 | semidirect |
| 85. C16 | C2×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×#595 | 2 |
| #11763735 | 2 |
| #11763721 | 2 |
| C16×#595 | 2 |
| D16×D17 | 2 |
| C4×D16 | 17 |