Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
828 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 828 conjugacy classes of subgroups — too many to draw. Only its 164 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 |
|---|---|---|
| 2. C22×C4×#595 | C2 | semidirect |
| 3. C2×(C2×#595)⋊C4 | C2 | semidirect |
| 4. C2×(C2×#595)⋊C4 | C2 | semidirect |
| 13. C2×C22⋊#595 | C4 | semidirect |
| 16. C2×C22⋊C4×C17 | C4 | semidirect |
| 17. C2×C22⋊Dic17 | C4 | semidirect |
| 18. C2×#63227 | C4 | semidirect |
| 19. C2×#63227 | C4 | semidirect |
| 71. C23×C17 | C42 | semidirect |
| 93. C22×D17 | C42 | semidirect |
| 115. C2×#595 | C22⋊C4 | semidirect |
| 119. C2×C4×C17 | C22⋊C4 | semidirect |
| 123. C2×Dic17 | C22⋊C4 | semidirect |
| 201. C2×C22⋊C4 | #595 | semidirect |
| 206. C17 | #1437 | semidirect |
| 283. C23 | C4×#595 | semidirect |
| 312. C2×C4 | C22⋊#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#595 | 2 |
| C22×C4×#595 | 2 |
| C2×(C2×#595)⋊C4 | 2 |
| C2×C22⋊C4×D17 | 2 |
| #1437 | 17 |