Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
604 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 181 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. C2×#10587555 | C2 | semidirect |
| 3. #11762734 | C2 | semidirect |
| 4. #11762714 | C2 | semidirect |
| 5. #11762669 | C2 | semidirect |
| 6. C4×C4⋊Dic17 | C2 | semidirect |
| 85. C4×C17 | #124 | semidirect |
| 117. C17 | #2547 | semidirect |
| 180. C4 | #10587622 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587555 | 2 |
| C2×#10587622 | 2 |
| #11762734 | 2 |
| #11762714 | 2 |
| #11762669 | 2 |
| C4×C4⋊Dic17 | 2 |
| C2×C4×D4×C17 | 2 |
| #2547 | 17 |