Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
280 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 13. #10587534 | C4 | semidirect |
| 14. C8×#595 | C4 | semidirect |
| 15. C17×#107 | C4 | semidirect |
| 16. #10587489 | C4 | semidirect |
| 17. #10587478 | C4 | semidirect |
| 59. C8×C17 | C42 | semidirect |
| 60. #3622 | C42 | semidirect |
| 71. #595 | #107 | direct (N × H) |
| 99. #107 | #595 | direct (N × H) |
| 102. C17 | C4×#107 | semidirect |
| 145. C8 | C4×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587534 | 2 |
| C2×C8×#595 | 2 |
| C4⋊C4×#595 | 2 |
| #11763682 | 2 |
| #107×D17 | 2 |
| C4×#107 | 17 |