Finite Group DatabasebetaFinite Group DatabasebetaOrder 1088.
298 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 159 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×M16×C17 | C2 | semidirect |
| 3. C2×#63223 | C2 | semidirect |
| 4. M16×D17 | C2 | direct (N × H) |
| 5. C2×#63218 | C2 | semidirect |
| 6. C2×C8×D17 | C2 | semidirect |
| 16. M16×C17 | C22 | semidirect |
| 17. C2×C8×C17 | C22 | semidirect |
| 18. #63223 | C22 | semidirect |
| 19. C2×#3622 | C22 | semidirect |
| 20. #63218 | C22 | semidirect |
| 21. C8×D17 | C22 | semidirect |
| 40. C8×C17 | C23 | semidirect |
| 41. #3622 | C23 | semidirect |
| 47. C2×D17 | M16 | direct (N × H) |
| 57. C2×C17 | C2×M16 | semidirect |
| 60. D17 | C2×M16 | direct (N × H) |
| 65. C2×M16 | D17 | direct (N × H) |
| 67. C17 | C22×M16 | semidirect |
| 79. M16 | C2×D17 | direct (N × H) |
| 82. C2×C8 | C2×D17 | semidirect |
| 102. C8 | C22×D17 | semidirect |
| 119. C2 | M16×D17 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D17 | 2 |
| C2×M16×C17 | 2 |
| C2×#63223 | 2 |
| M16×D17 | 2 |
| C2×#63218 | 2 |
| C2×C8×D17 | 2 |
| C22×M16 | 17 |