Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
182 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 56 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. #22578437 | C2 | semidirect |
| 2. D4×#11764047 | C2 | semidirect |
| 3. #22578264 | C2 | semidirect |
| 4. #22578251 | C2 | semidirect |
| 5. D4⋊#11764047 | C2 | semidirect |
| 6. #22578245 | C2 | semidirect |
| 60. D4×C137 | M16 | semidirect |
| 83. C137 | #1586 | semidirect |
| 131. D4 | #14555520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578437 | 2 |
| D4×#11764047 | 2 |
| #22578264 | 2 |
| #22578251 | 2 |
| D4⋊#11764047 | 2 |
| #22578245 | 2 |
| #22577483 | 2 |
| #1586 | 137 |