Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
438 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 80 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×D4×#595 | C2 | semidirect |
| 2. C2×#10587547 | C2 | semidirect |
| 3. C2×#10587547 | C2 | semidirect |
| 4. #11763761 | C2 | semidirect |
| 5. #11763683 | C2 | semidirect |
| 6. #11763674 | C2 | semidirect |
| 20. C2×D8×C17 | C4 | semidirect |
| 21. C2×#63228 | C4 | semidirect |
| 22. C2×#63228 | C4 | semidirect |
| 25. C2×D136 | C4 | semidirect |
| 39. C2×D4×C17 | C2×C4 | semidirect |
| 51. C2×D68 | C2×C4 | semidirect |
| 66. C2×C8×C17 | C2×C4 | semidirect |
| 69. C2×#3622 | C2×C4 | semidirect |
| 102. C2×#595 | D8 | semidirect |
| 106. D4×C17 | C22⋊C4 | semidirect |
| 116. D68 | C22⋊C4 | semidirect |
| 186. C2×D8 | #595 | semidirect |
| 199. C17 | #1879 | semidirect |
| 215. C2×D4 | C2×#595 | semidirect |
| 234. C2×C8 | C2×#595 | semidirect |
| 272. D4 | C22⋊#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#595 | 2 |
| C2×#10587547 | 2 |
| #11763761 | 2 |
| #11763683 | 2 |
| #11763674 | 2 |
| C2×D8×D17 | 2 |
| #1879 | 17 |