Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
220 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 47 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. #22578205 | C2 | semidirect |
| 2. #22577838 | C2 | semidirect |
| 3. C2×D2192 | C2 | semidirect |
| 4. #22577674 | C2 | semidirect |
| 5. #22577215 | C2 | semidirect |
| 6. #22577186 | C2 | semidirect |
| 7. #359×C137 | C2 | semidirect |
| 14. C2×D1096 | C22 | semidirect |
| 20. #17984028 | C22 | semidirect |
| 23. C2×C16×C137 | C22 | semidirect |
| 24. #108×C137 | C22 | semidirect |
| 93. C137 | #2192 | semidirect |
| 100. #359 | D137 | semidirect |
| 116. C2×C16 | C2×D137 | semidirect |
| 117. #108 | C2×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578205 | 2 |
| #22577838 | 2 |
| C2×D2192 | 2 |
| #22577674 | 2 |
| #22577215 | 2 |
| #22577186 | 2 |
| #359×C137 | 2 |
| #2192 | 137 |