Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
162 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
| 4. #22577155 | C2 | semidirect |
| 6. #22577125 | C2 | semidirect |
| 7. Q8⋊C8×C137 | C2 | semidirect |
| 51. #11764040 | M16 | semidirect |
| 77. C137 | #1592 | semidirect |
| 83. Q8⋊C8 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577534 | 2 |
| C4×#14555497 | 2 |
| #22577480 | 2 |
| #22577155 | 2 |
| #22577132 | 2 |
| #22577125 | 2 |
| Q8⋊C8×C137 | 2 |
| #1592 | 137 |