Finite Group DatabasebetaFinite Group DatabasebetaOrder 1088.
124 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 46 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 |
|---|---|---|
| 1. C2×#63243 | C2 | semidirect |
| 2. C2×#63242 | C2 | semidirect |
| 4. #10587544 | C2 | semidirect |
| 5. #10587543 | C2 | semidirect |
| 6. #10587543 | C2 | semidirect |
| 7. #10587542 | C2 | semidirect |
| 36. #3624 | D4 | semidirect |
| 43. C2×D17 | M16 | semidirect |
| 63. C17 | #435 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63243 | 2 |
| C2×#63242 | 2 |
| #10587579 | 2 |
| #10587544 | 2 |
| #10587543 | 2 |
| #10587542 | 2 |
| #435 | 17 |