Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
166 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22577530 | C2 | semidirect |
| 4. #22577153 | C2 | semidirect |
| 5. #22577135 | C2 | semidirect |
| 6. C8×#11764040 | C2 | semidirect |
| 48. #11764040 | M16 | semidirect |
| 49. #11764040 | SD16 | semidirect |
| 77. C137 | #1590 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577530 | 2 |
| C4×#14555498 | 2 |
| #22577481 | 2 |
| #22577153 | 2 |
| #22577135 | 2 |
| C8×#11764040 | 2 |
| D4⋊C8×C137 | 2 |
| #1590 | 137 |