Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
480 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 181 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×#17984088 | C2 | semidirect |
| 2. #22577683 | C2 | direct (N × H) |
| 3. C2×#17984021 | C2 | semidirect |
| 4. C2×C4⋊#11764040 | C2 | semidirect |
| 10. #17984088 | C22 | semidirect |
| 13. #17984021 | C22 | semidirect |
| 14. C4⋊#11764040 | C22 | semidirect |
| 34. C2×D4×C137 | Q8 | semidirect |
| 58. D4×C137 | C2×Q8 | semidirect |
| 86. C2×C137 | #474 | semidirect |
| 90. C137 | C2×#474 | semidirect |
| 119. C2×D4 | Dic274 | semidirect |
| 146. D4 | C2×Dic274 | semidirect |
| 177. C2 | #22577683 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984088 | 2 |
| #22577683 | 2 |
| C2×#17984021 | 2 |
| C2×C4⋊#11764040 | 2 |
| C2×#17984009 | 2 |
| C2×C4×D4×C137 | 2 |
| C2×#474 | 137 |