Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
528 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 274 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. #11763825 | C2 | direct (N × H) |
| 2. C2×C4⋊#3624 | C2 | semidirect |
| 4. C2×C4×#3624 | C2 | semidirect |
| 17. C4⋊#3624 | C22 | semidirect |
| 18. C4×#3624 | C22 | semidirect |
| 20. C22×C4×C17 | C8 | semidirect |
| 48. C2×C4×C17 | C2×C8 | semidirect |
| 86. C2×C17 | #431 | semidirect |
| 103. C17 | C2×#431 | semidirect |
| 114. C22×C4 | #3624 | semidirect |
| 145. C2×C4 | C2×#3624 | semidirect |
| 165. C2 | #11763825 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763825 | 2 |
| C2×C4⋊#3624 | 2 |
| C2×C22⋊#3624 | 2 |
| C2×C4×#3624 | 2 |
| C22×C4×Dic17 | 2 |
| C2×#431 | 17 |