Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22578118 | C2 | semidirect |
| 2. #22578058 | C2 | semidirect |
| 3. #22577801 | C2 | semidirect |
| 4. #22577726 | C2 | semidirect |
| 5. #22577720 | C2 | semidirect |
| 6. #22577693 | C2 | semidirect |
| 7. #22577683 | C2 | semidirect |
| 8. #22577653 | C2 | semidirect |
| 9. #22577482 | C2 | semidirect |
| 10. #22577444 | C2 | semidirect |
| 11. C4×D8×C137 | C2 | semidirect |
| 101. C8×C137 | #41 | semidirect |
| 127. C137 | #3354 | semidirect |
| 137. C4×D8 | D137 | semidirect |
| 229. C8 | #14555510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578118 | 2 |
| #22578058 | 2 |
| #22577801 | 2 |
| #22577726 | 2 |
| #22577720 | 2 |
| #22577693 | 2 |
| #22577683 | 2 |
| #22577653 | 2 |
| #22577482 | 2 |
| #22577444 | 2 |
| C4×D8×C137 | 2 |
| #3354 | 137 |