Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
284 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 73 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×C22⋊#11764040 | C2 | semidirect |
| 3. #22577139 | C2 | semidirect |
| 4. #22577136 | C2 | semidirect |
| 5. #381×C137 | C2 | semidirect |
| 6. C2×#14555510 | C4 | semidirect |
| 9. #17984067 | C4 | semidirect |
| 11. #17984062 | C4 | semidirect |
| 16. #17984047 | C4 | semidirect |
| 111. C137 | #1516 | semidirect |
| 115. #381 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577914 | 2 |
| C2×C22⋊#11764040 | 2 |
| #22577139 | 2 |
| #22577136 | 2 |
| #381×C137 | 2 |
| #1516 | 137 |