Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
384 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 126 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. C2×C8×#595 | C2 | semidirect |
| 4. #11763674 | C2 | semidirect |
| 10. C22×C8×C17 | C4 | semidirect |
| 11. C22×#3622 | C4 | semidirect |
| 13. C2×C8×D17 | C4 | semidirect |
| 14. C2×C8×D17 | C4 | semidirect |
| 17. C22⋊#3624 | C4 | semidirect |
| 19. #10587543 | C4 | semidirect |
| 31. C22⋊#595 | C8 | direct (N × H) |
| 55. C2×#595 | C2×C8 | semidirect |
| 71. C8×C17 | C22⋊C4 | semidirect |
| 73. #3622 | C22⋊C4 | semidirect |
| 77. C22×C17 | C4×C8 | semidirect |
| 82. C2×D17 | C4×C8 | semidirect |
| 111. C22×C8 | #595 | semidirect |
| 118. C17 | C8×C22⋊C4 | semidirect |
| 171. C8 | C22⋊#595 | direct (N × H) |
| 181. C22 | C8×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763777 | 2 |
| C2×C8×#595 | 2 |
| C4×C22⋊#595 | 2 |
| #11763674 | 2 |
| C22×C8×D17 | 2 |
| C8×C22⋊C4 | 17 |