Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
738 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 198 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. #11763888 | C2 | semidirect |
| 2. #41×#595 | C2 | semidirect |
| 3. #11763807 | C2 | semidirect |
| 4. #11763806 | C2 | semidirect |
| 5. D17⋊#104 | C2 | semidirect |
| 6. C2×#10587548 | C2 | semidirect |
| 8. C17×H(5,𝔽2) | C4 | semidirect |
| 10. #10587697 | C4 | semidirect |
| 11. #10587697 | C4 | semidirect |
| 16. #10587691 | C4 | semidirect |
| 23. #10587677 | C22 | semidirect |
| 24. C2×C4×#595 | C22 | semidirect |
| 25. D17⋊M16 | C22 | semidirect |
| 26. C2×#63243 | C22 | semidirect |
| 27. #10587550 | C22 | semidirect |
| 28. #10587550 | C22 | semidirect |
| 29. #10587548 | C22 | semidirect |
| 30. #10587548 | C22 | semidirect |
| 31. #10587548 | C22 | semidirect |
| 35. #41×C17 | C2×C4 | semidirect |
| 37. C2×D4×C17 | C2×C4 | semidirect |
| 44. Q8×D17 | C2×C4 | semidirect |
| 52. #63254 | C2×C4 | semidirect |
| 57. D4×D17 | C2×C4 | semidirect |
| 62. #63252 | C2×C4 | semidirect |
| 66. C2×Dic34 | C2×C4 | semidirect |
| 152. H(5,𝔽2) | #595 | semidirect |
| 171. C17 | #2901 | semidirect |
| 189. #41 | C2×#595 | semidirect |
| 202. C2×D4 | C2×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763888 | 2 |
| #41×#595 | 2 |
| #11763807 | 2 |
| #11763806 | 2 |
| D17⋊#104 | 2 |
| C2×#10587548 | 2 |
| #11763644 | 2 |
| #2901 | 17 |