Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
296 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 13. #10587507 | C4 | direct (N × H) |
| 59. C4×C17 | #101 | semidirect |
| 81. C17 | C4×#101 | semidirect |
| 124. C4 | #10587507 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587507 | 2 |
| C4×#63223 | 2 |
| #11762578 | 2 |
| C2×C4×Q8×C17 | 2 |
| C4×#101 | 17 |