Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
316 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 72 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. #11763830 | C2 | semidirect |
| 2. C4×#63247 | C2 | semidirect |
| 3. D4⋊#3624 | C2 | semidirect |
| 18. C4⋊#3624 | C22 | semidirect |
| 19. C4×#3624 | C22 | semidirect |
| 49. D4×C17 | M16 | semidirect |
| 105. C17 | #1490 | semidirect |
| 135. D4 | #63247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763830 | 2 |
| C4×#63247 | 2 |
| D4⋊#3624 | 2 |
| C2×D4×Dic17 | 2 |
| #1490 | 17 |