Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
840 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 840 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 |
|---|---|---|
| 1. C2×#17984064 | C2 | semidirect |
| 3. #22577322 | C2 | semidirect |
| 4. #22577314 | C2 | semidirect |
| 5. #22577310 | C2 | semidirect |
| 7. #22577276 | C2 | semidirect |
| 8. #22577263 | C2 | semidirect |
| 9. C23×Q8×C137 | C2 | semidirect |
| 34. C2×C22⋊D137 | Q8 | semidirect |
| 55. C2×Q8×C137 | D4 | semidirect |
| 67. C22×D137 | C2×Q8 | semidirect |
| 78. C2×Dic137 | C2×Q8 | semidirect |
| 101. C22×C137 | C22⋊Q8 | semidirect |
| 126. C137 | #2409 | semidirect |
| 128. C23×Q8 | D137 | semidirect |
| 165. C2×Q8 | C22⋊D137 | semidirect |
| 233. C22 | #17984064 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984064 | 2 |
| C2×C4×C22⋊D137 | 2 |
| #22577322 | 2 |
| #22577314 | 2 |
| #22577310 | 2 |
| #22577282 | 2 |
| #22577276 | 2 |
| #22577263 | 2 |
| C23×Q8×C137 | 2 |
| #2409 | 137 |