Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
656 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 197 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. C22×#63230 | C2 | semidirect |
| 3. #11763183 | C2 | direct (N × H) |
| 4. C2×C4×#3622 | C2 | semidirect |
| 5. C2×C17×C4⋊Q8 | C2 | semidirect |
| 10. C17×C4⋊Q8 | C22 | semidirect |
| 14. C2×#63230 | C22 | semidirect |
| 18. C4×#3622 | C22 | semidirect |
| 35. C2×#3622 | D4 | semidirect |
| 45. C2×C4×C17 | SD16 | semidirect |
| 53. #3622 | C2×D4 | semidirect |
| 63. C4×C17 | C2×SD16 | semidirect |
| 66. C2×C4⋊Q8 | D17 | semidirect |
| 70. C2×C17 | #492 | semidirect |
| 81. C4⋊Q8 | C2×D17 | semidirect |
| 87. C17 | C2×#492 | semidirect |
| 117. C2×C4 | #63230 | semidirect |
| 131. C4 | C2×#63230 | semidirect |
| 134. C2 | #11763183 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63230 | 2 |
| C2×#10587560 | 2 |
| #11763183 | 2 |
| C2×C4×#3622 | 2 |
| C2×C17×C4⋊Q8 | 2 |
| C2×#492 | 17 |