Finite Group DatabasebetaFinite Group DatabasebetaOrder 1088.
170 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 52 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×C4×#595 | C2 | semidirect |
| 3. C2×#63243 | C2 | semidirect |
| 4. #10587550 | C2 | direct (N × H) |
| 6. C2×Q8×C17 | C4 | semidirect |
| 9. #63256 | C4 | semidirect |
| 12. C2×D68 | C4 | semidirect |
| 17. C4×#595 | C22 | semidirect |
| 19. #63243 | C22 | semidirect |
| 25. Q8×C17 | C2×C4 | semidirect |
| 32. D68 | C2×C4 | semidirect |
| 53. C2×C17 | #104 | semidirect |
| 62. C17 | C2×#104 | semidirect |
| 67. C2×Q8 | #595 | semidirect |
| 81. Q8 | C2×#595 | semidirect |
| 113. C2 | #10587550 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63256 | 2 |
| C2×C4×#595 | 2 |
| C2×#63243 | 2 |
| #10587550 | 2 |
| C2×#104 | 17 |