Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
224 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 62 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. #11763865 | C2 | semidirect |
| 2. #11763819 | C2 | semidirect |
| 3. #11763726 | C2 | semidirect |
| 7. C2×Q16×C17 | C4 | semidirect |
| 11. #10587605 | C4 | semidirect |
| 13. C2×D136 | C4 | semidirect |
| 17. #10587533 | C22 | semidirect |
| 18. #10587530 | C22 | semidirect |
| 94. C2×Q16 | #595 | semidirect |
| 104. C17 | #2145 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763865 | 2 |
| #11763819 | 2 |
| #11763726 | 2 |
| C2×#10587605 | 2 |
| #2145 | 17 |