Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
384 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 82 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. C2×#10587534 | C2 | semidirect |
| 2. C2×#10587547 | C2 | semidirect |
| 3. C2×C8×#595 | C2 | semidirect |
| 4. #11763761 | C2 | semidirect |
| 11. C2×D8×C17 | C4 | semidirect |
| 12. C2×#63228 | C4 | semidirect |
| 15. C2×D136 | C4 | semidirect |
| 57. C2×#595 | D8 | semidirect |
| 71. C8×C17 | C22⋊C4 | semidirect |
| 72. #3622 | C22⋊C4 | semidirect |
| 109. C2×D8 | #595 | semidirect |
| 118. C17 | #1970 | semidirect |
| 171. C8 | C22⋊#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×#10587547 | 2 |
| C2×C8×#595 | 2 |
| #11763761 | 2 |
| C2×D8×D17 | 2 |
| #1970 | 17 |