Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22577443 | C2 | semidirect |
| 5. #22577164 | C2 | semidirect |
| 6. #22577162 | C2 | semidirect |
| 7. #428×C137 | C2 | semidirect |
| 20. #17984004 | C4 | semidirect |
| 37. #14555494 | C2×C4 | semidirect |
| 51. M16×C137 | C2×C4 | semidirect |
| 114. C137 | #1856 | semidirect |
| 118. #428 | D137 | semidirect |
| 156. M16 | C4×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577877 | 2 |
| #22577443 | 2 |
| C2×#17984004 | 2 |
| #22577304 | 2 |
| #22577164 | 2 |
| #22577162 | 2 |
| #428×C137 | 2 |
| #1856 | 137 |