Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
600 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 258 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×#10587534 | C2 | direct (N × H) |
| 8. C22×C8×C17 | C4 | semidirect |
| 9. C22×#3622 | C4 | semidirect |
| 10. C2×C8×D17 | C4 | semidirect |
| 12. #10587534 | C22 | direct (N × H) |
| 24. C2×C8×C17 | C2×C4 | semidirect |
| 25. C2×#3622 | C2×C4 | semidirect |
| 26. C8×D17 | C2×C4 | semidirect |
| 44. C8×C17 | C22×C4 | semidirect |
| 45. #3622 | C22×C4 | semidirect |
| 47. C22×C17 | #107 | semidirect |
| 49. C2×D17 | #107 | semidirect |
| 62. C2×C17 | C2×#107 | semidirect |
| 64. D17 | C2×#107 | semidirect |
| 72. C22×C8 | #595 | semidirect |
| 76. C17 | C22×#107 | semidirect |
| 89. C2×C8 | C2×#595 | semidirect |
| 109. C8 | C22×#595 | semidirect |
| 115. C22 | #10587534 | direct (N × H) |
| 125. C2 | C2×#10587534 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#595 | 2 |
| C2×#10587534 | 2 |
| C22×C8×D17 | 2 |
| C22×#107 | 17 |