Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
832 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 832 conjugacy classes of subgroups — too many to draw. Only its 209 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×C4×C22⋊D137 | C2 | semidirect |
| 3. C2×#17984048 | C2 | semidirect |
| 4. #22577303 | C2 | semidirect |
| 5. #22577303 | C2 | semidirect |
| 6. #22577283 | C2 | semidirect |
| 7. #22577281 | C2 | semidirect |
| 8. #22577254 | C2 | semidirect |
| 9. #386×C137 | C2 | semidirect |
| 15. #17984084 | C4 | semidirect |
| 37. C2×D548 | C2×C4 | semidirect |
| 42. C2×C22⋊D137 | C2×C4 | semidirect |
| 43. C2×C22⋊D137 | C2×C4 | semidirect |
| 53. #14555489 | D4 | semidirect |
| 61. C4×Dic137 | C2×C4 | semidirect |
| 66. C2×D4×C137 | C2×C4 | semidirect |
| 144. Dic137 | C4×D4 | semidirect |
| 153. C137 | #2366 | semidirect |
| 162. #386 | D137 | semidirect |
| 202. C2×D4 | C4×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984084 | 2 |
| C2×C4×C22⋊D137 | 2 |
| C2×#17984048 | 2 |
| #22577303 | 2 |
| #22577283 | 2 |
| #22577281 | 2 |
| #22577254 | 2 |
| #386×C137 | 2 |
| #2366 | 137 |