Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
272 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
| 20. #10587479 | C4 | semidirect |
| 21. #10587478 | C4 | semidirect |
| 73. #3622 | C42 | semidirect |
| 120. C17 | #1776 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587478 | 2 |
| C2×#10587479 | 2 |
| C2×#10587486 | 2 |
| C4⋊C4×Dic17 | 2 |
| #11762572 | 2 |
| C17×#340 | 2 |
| #1776 | 17 |