Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
572 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 153 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×#17984110 | C2 | semidirect |
| 2. C2×#17984108 | C2 | semidirect |
| 3. #22577949 | C2 | semidirect |
| 4. #22577788 | C2 | semidirect |
| 5. #22577786 | C2 | semidirect |
| 6. #22577784 | C2 | semidirect |
| 7. #22577781 | C2 | semidirect |
| 8. #22577778 | C2 | semidirect |
| 9. #22577774 | C2 | semidirect |
| 10. C2×C8×Dic137 | C2 | semidirect |
| 11. C2×#135×C137 | C2 | semidirect |
| 55. C2×#11764040 | D4 | semidirect |
| 74. C2×C8×C137 | D4 | semidirect |
| 119. Dic137 | #135 | semidirect |
| 125. C137 | #3147 | semidirect |
| 129. C2×#135 | D137 | semidirect |
| 194. C2×C8 | C22⋊D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984110 | 2 |
| C2×#17984108 | 2 |
| #22577949 | 2 |
| #22577788 | 2 |
| #22577786 | 2 |
| #22577784 | 2 |
| #22577781 | 2 |
| #22577778 | 2 |
| #22577774 | 2 |
| C2×C8×Dic137 | 2 |
| C2×#135×C137 | 2 |
| #3147 | 137 |