Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
1492 conjugacy classes of subgroups; only the 754 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 754 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. #11763878 | C2 | semidirect |
| 2. #11763877 | C2 | semidirect |
| 3. #41×#595 | C2 | semidirect |
| 4. C2×Q8×#595 | C2 | semidirect |
| 6. C17×2−1+4 | C4 | semidirect |
| 7. #10587697 | C4 | semidirect |
| 9. #10587694 | C4 | semidirect |
| 21. #41×C17 | C2×C4 | semidirect |
| 22. C2×Q8×C17 | C2×C4 | semidirect |
| 23. #63256 | C2×C4 | semidirect |
| 24. Q8×D17 | C2×C4 | semidirect |
| 26. #63254 | C2×C4 | semidirect |
| 28. #63252 | C2×C4 | semidirect |
| 30. C2×Dic34 | C2×C4 | semidirect |
| 59. #595 | 2−1+4 | direct (N × H) |
| 74. 2−1+4 | #595 | direct (N × H) |
| 85. C17 | C4×2−1+4 | semidirect |
| 89. #41 | C2×#595 | semidirect |
| 93. C2×Q8 | C2×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763878 | 2 |
| #11763877 | 2 |
| #41×#595 | 2 |
| C2×Q8×#595 | 2 |
| 2−1+4×D17 | 2 |
| C4×2−1+4 | 17 |