Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
1008 conjugacy classes of subgroups; only the 242 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 242 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×#63243 | C2 | semidirect |
| 2. #11763780 | C2 | direct (N × H) |
| 3. C2×#10587543 | C2 | semidirect |
| 4. C2×C22⋊#3624 | C2 | semidirect |
| 16. C22×#3624 | C22 | semidirect |
| 18. C2×#63243 | C22 | semidirect |
| 19. C22⋊#3624 | C22 | semidirect |
| 20. #10587543 | C22 | semidirect |
| 50. C2×#3624 | C23 | semidirect |
| 54. C23×C17 | M16 | semidirect |
| 66. C22×D17 | M16 | semidirect |
| 95. C22×C17 | C2×M16 | semidirect |
| 105. C2×D17 | C2×M16 | semidirect |
| 117. C2×C17 | #407 | semidirect |
| 138. C17 | C2×#407 | semidirect |
| 184. C23 | #63243 | semidirect |
| 219. C22 | C2×#63243 | semidirect |
| 231. C2 | #11763780 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63243 | 2 |
| #11763780 | 2 |
| C2×#10587543 | 2 |
| C2×C22⋊#3624 | 2 |
| C23×C4×D17 | 2 |
| C2×#407 | 17 |