Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
1168 conjugacy classes of subgroups; only the 541 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 541 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. #22577959 | C2 | direct (N × H) |
| 2. C2×#17984087 | C2 | semidirect |
| 3. C2×#17984080 | C2 | semidirect |
| 5. C2×#17984053 | C2 | semidirect |
| 8. C2×#125×C137 | C2 | semidirect |
| 12. #17984087 | C22 | semidirect |
| 13. #17984080 | C22 | semidirect |
| 15. #17984053 | C22 | semidirect |
| 25. #125×C137 | C22 | semidirect |
| 36. C2×C4×D137 | Q8 | semidirect |
| 63. C4×D137 | C2×Q8 | semidirect |
| 83. C2×C137 | #533 | semidirect |
| 87. C137 | C2×#533 | semidirect |
| 92. C2×#125 | D137 | semidirect |
| 102. #125 | C2×D137 | semidirect |
| 172. C2 | #22577959 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577959 | 2 |
| C2×#17984087 | 2 |
| C2×#17984080 | 2 |
| C2×#17984066 | 2 |
| C2×#17984053 | 2 |
| C2×#17984046 | 2 |
| C2×C42×D137 | 2 |
| C2×#125×C137 | 2 |
| C2×#533 | 137 |