Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
572 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 288 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. #22578368 | C2 | semidirect |
| 3. C4×#14555520 | C2 | semidirect |
| 4. C4×#14555518 | C2 | semidirect |
| 6. #17984176 | C4 | direct (N × H) |
| 20. #14555520 | C2×C4 | semidirect |
| 21. #14555518 | C2×C4 | semidirect |
| 57. C4×C137 | #131 | semidirect |
| 59. Dic137 | #131 | semidirect |
| 65. C137 | C4×#131 | semidirect |
| 126. C4 | #17984176 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984176 | 2 |
| #22578368 | 2 |
| C4×#14555520 | 2 |
| C4×#14555518 | 2 |
| C4×#14555511 | 2 |
| C4×#131 | 137 |