Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
162 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22577534 | C2 | semidirect |
| 3. #22577156 | C2 | semidirect |
| 4. Q8⋊#11764040 | C2 | semidirect |
| 6. #22577124 | C2 | semidirect |
| 60. C8×C137 | M16 | semidirect |
| 77. C137 | #1592 | semidirect |
| 138. C8 | #14555494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577534 | 2 |
| #22577481 | 2 |
| #22577156 | 2 |
| Q8⋊#11764040 | 2 |
| D4⋊#11764040 | 2 |
| #22577124 | 2 |
| C4×SD16×C137 | 2 |
| #1592 | 137 |