Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
332 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 66 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. #41×#595 | C2 | semidirect |
| 2. #11763806 | C2 | semidirect |
| 3. C2×#10587550 | C2 | semidirect |
| 4. #11763790 | C2 | semidirect |
| 5. #11763692 | C2 | semidirect |
| 6. #11763681 | C2 | semidirect |
| 19. C17×#137 | C4 | semidirect |
| 20. #10587635 | C4 | semidirect |
| 21. #10587628 | C4 | semidirect |
| 26. #10587594 | C4 | semidirect |
| 36. C2×Q8×C17 | C2×C4 | semidirect |
| 50. C2×D68 | C2×C4 | semidirect |
| 71. M16×C17 | C2×C4 | semidirect |
| 76. #63223 | C2×C4 | semidirect |
| 162. #137 | #595 | semidirect |
| 183. C17 | #1906 | semidirect |
| 195. C2×Q8 | C2×#595 | semidirect |
| 217. M16 | C2×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×#595 | 2 |
| #11763806 | 2 |
| C2×#10587550 | 2 |
| #11763790 | 2 |
| #11763692 | 2 |
| #11763681 | 2 |
| #11763608 | 2 |
| #1906 | 17 |