Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
256 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 19. #10587486 | C4 | semidirect |
| 63. C8×C17 | C4⋊C4 | semidirect |
| 64. #3622 | C4⋊C4 | semidirect |
| 106. C17 | #1847 | semidirect |
| 149. C8 | #63225 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587478 | 2 |
| C2×#10587488 | 2 |
| C2×#10587479 | 2 |
| C2×#10587486 | 2 |
| #11762678 | 2 |
| #11762674 | 2 |
| C2×C17×#107 | 2 |
| #1847 | 17 |