Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
516 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 3. #22577287 | C2 | semidirect |
| 4. #22577271 | C2 | semidirect |
| 5. C4×#14555489 | C2 | semidirect |
| 7. C43×C137 | C2 | semidirect |
| 9. #17984082 | C4 | direct (N × H) |
| 28. #14555489 | C2×C4 | semidirect |
| 37. C42×C137 | C2×C4 | semidirect |
| 65. C4×C137 | #126 | semidirect |
| 73. C137 | C4×#126 | semidirect |
| 81. C43 | D137 | semidirect |
| 111. C42 | C4×D137 | semidirect |
| 142. C4 | #17984082 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984082 | 2 |
| #22577294 | 2 |
| #22577287 | 2 |
| #22577271 | 2 |
| C4×#14555489 | 2 |
| C4×#14555487 | 2 |
| C43×C137 | 2 |
| C4×#126 | 137 |