Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
652 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 182 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. C2×Q8×#595 | C2 | semidirect |
| 3. (C2×#595)⋊Q8 | C2 | semidirect |
| 5. #11763759 | C2 | semidirect |
| 6. #11763753 | C2 | semidirect |
| 7. C22⋊C4×#595 | C2 | semidirect |
| 8. C42×#595 | C2 | semidirect |
| 25. C17×#124 | C4 | semidirect |
| 26. #10587633 | C4 | semidirect |
| 27. #10587622 | C4 | semidirect |
| 28. #10587571 | C4 | semidirect |
| 30. #10587561 | C4 | semidirect |
| 42. C2×Q8×C17 | C2×C4 | semidirect |
| 53. C2×Dic34 | C2×C4 | semidirect |
| 54. C2×Dic34 | C2×C4 | semidirect |
| 65. C22⋊C4×C17 | C2×C4 | semidirect |
| 66. C42×C17 | C2×C4 | semidirect |
| 67. C22⋊Dic17 | C2×C4 | semidirect |
| 68. #63227 | C2×C4 | semidirect |
| 69. #63227 | C2×C4 | semidirect |
| 70. C4×Dic17 | C2×C4 | semidirect |
| 71. C4×Dic17 | C2×C4 | semidirect |
| 126. #595 | #124 | direct (N × H) |
| 156. #124 | #595 | direct (N × H) |
| 173. C17 | C4×#124 | semidirect |
| 179. C2×Q8 | C2×#595 | semidirect |
| 203. C22⋊C4 | C2×#595 | semidirect |
| 211. C42 | C2×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#595 | 2 |
| C2×D4×#595 | 2 |
| (C2×#595)⋊Q8 | 2 |
| #11763761 | 2 |
| #11763759 | 2 |
| #11763753 | 2 |
| C22⋊C4×#595 | 2 |
| C42×#595 | 2 |
| #124×D17 | 2 |
| C4×#124 | 17 |