Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
480 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 181 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×#10587555 | C2 | semidirect |
| 2. #11763089 | C2 | direct (N × H) |
| 3. C2×#10587478 | C2 | semidirect |
| 4. C2×C4⋊#3622 | C2 | semidirect |
| 19. #10587555 | C22 | semidirect |
| 21. #10587478 | C22 | semidirect |
| 22. C4⋊#3622 | C22 | semidirect |
| 26. C2×D4×C17 | Q8 | semidirect |
| 54. D4×C17 | C2×Q8 | semidirect |
| 93. C2×C17 | #474 | semidirect |
| 113. C17 | C2×#474 | semidirect |
| 119. C2×D4 | Dic34 | semidirect |
| 146. D4 | C2×Dic34 | semidirect |
| 177. C2 | #11763089 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587555 | 2 |
| #11763089 | 2 |
| C2×#10587478 | 2 |
| C2×C4⋊#3622 | 2 |
| C2×#10587503 | 2 |
| C2×C4×D4×C17 | 2 |
| C2×#474 | 17 |