Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
1008 conjugacy classes of subgroups; only the 250 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 250 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. #11763779 | C2 | direct (N × H) |
| 3. C2×C22⋊#3624 | C2 | semidirect |
| 14. C2×#63247 | C22 | semidirect |
| 15. C22×#3624 | C22 | semidirect |
| 16. C22⋊#3624 | C22 | semidirect |
| 39. C2×#3624 | C23 | semidirect |
| 47. C23×C17 | M16 | semidirect |
| 75. C22×C17 | C2×M16 | semidirect |
| 87. C2×C17 | #407 | semidirect |
| 102. C17 | C2×#407 | semidirect |
| 132. C23 | #63247 | semidirect |
| 158. C22 | C2×#63247 | semidirect |
| 168. C2 | #11763779 | 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 |
| #11763779 | 2 |
| C2×C22⋊#3624 | 2 |
| C24×Dic17 | 2 |
| C2×#407 | 17 |