Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
452 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 137 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. #22578203 | C2 | semidirect |
| 2. C2×#17984110 | C2 | semidirect |
| 3. C2×#17984094 | C2 | semidirect |
| 4. #22577679 | C2 | semidirect |
| 5. #22577674 | C2 | semidirect |
| 6. #22577667 | C2 | semidirect |
| 7. #22577385 | C2 | semidirect |
| 8. C2×#108×C137 | C2 | semidirect |
| 20. C2×Dic548 | C22 | semidirect |
| 21. C2×#14555499 | C22 | semidirect |
| 22. C2×D1096 | C22 | semidirect |
| 30. #17984006 | C22 | semidirect |
| 31. #17984004 | C22 | semidirect |
| 34. #108×C137 | C22 | semidirect |
| 35. #108×C137 | C22 | semidirect |
| 132. C137 | #3067 | semidirect |
| 140. C2×#108 | D137 | semidirect |
| 165. #108 | C2×D137 | semidirect |
| 166. #108 | C2×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578203 | 2 |
| C2×#17984110 | 2 |
| C2×#17984094 | 2 |
| #22577679 | 2 |
| #22577674 | 2 |
| #22577667 | 2 |
| #22577385 | 2 |
| C2×#108×C137 | 2 |
| #3067 | 137 |