Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
164 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 66 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. C2×#17984163 | C2 | semidirect |
| 2. C22×#14555513 | C2 | semidirect |
| 3. #22578324 | C2 | semidirect |
| 4. #22578298 | C2 | semidirect |
| 5. C22⋊#14555513 | C2 | semidirect |
| 6. #22578292 | C2 | semidirect |
| 24. #14555513 | D4 | semidirect |
| 59. C22×C137 | M32 | semidirect |
| 75. C137 | #2168 | semidirect |
| 138. C22 | #17984163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984163 | 2 |
| C22×#14555513 | 2 |
| #22578324 | 2 |
| #22578298 | 2 |
| C22⋊#14555513 | 2 |
| #22578292 | 2 |
| #22577466 | 2 |
| #2168 | 137 |