Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
564 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 186 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. C22×#63247 | C2 | semidirect |
| 2. C22×#63242 | C2 | semidirect |
| 3. #11763841 | C2 | direct (N × H) |
| 4. C2×C4⋊#3624 | C2 | semidirect |
| 5. C2×#10587543 | C2 | semidirect |
| 6. C2×C22⋊#3624 | C2 | semidirect |
| 7. C2×#10587542 | C2 | semidirect |
| 13. C2×#63247 | C22 | semidirect |
| 19. C2×#63242 | C22 | semidirect |
| 26. C22⋊#3624 | C22 | semidirect |
| 27. #10587543 | C22 | semidirect |
| 28. #10587542 | C22 | semidirect |
| 29. C4⋊#3624 | C22 | semidirect |
| 51. C2×#3624 | D4 | semidirect |
| 69. C22×D17 | M16 | semidirect |
| 93. #3624 | C2×D4 | semidirect |
| 106. C2×D17 | C2×M16 | semidirect |
| 123. C2×C17 | #435 | semidirect |
| 149. C17 | C2×#435 | semidirect |
| 235. C2 | #11763841 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63247 | 2 |
| C22×#63242 | 2 |
| #11763841 | 2 |
| C2×C4⋊#3624 | 2 |
| C2×#10587543 | 2 |
| C2×C22⋊#3624 | 2 |
| C2×#10587542 | 2 |
| C2×#10587567 | 2 |
| C2×#435 | 17 |