Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
572 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 173 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×#17984110 | C2 | semidirect |
| 2. #22577953 | C2 | semidirect |
| 3. #22577787 | C2 | semidirect |
| 4. #22577783 | C2 | semidirect |
| 5. #22577780 | C2 | semidirect |
| 6. #22577776 | C2 | semidirect |
| 7. C2×C4×C8×C137 | C2 | semidirect |
| 36. C2×C8×C137 | D4 | semidirect |
| 65. C4×C137 | #135 | semidirect |
| 72. C137 | #3147 | semidirect |
| 80. C2×C4×C8 | D137 | semidirect |
| 107. C2×C8 | D548 | semidirect |
| 139. C4 | #17984110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984110 | 2 |
| #22577953 | 2 |
| #22577787 | 2 |
| #22577783 | 2 |
| #22577780 | 2 |
| #22577776 | 2 |
| C2×C4×C8×C137 | 2 |
| #3147 | 137 |