Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
164 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 55 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×#17984032 | C2 | semidirect |
| 2. C22×#14555485 | C2 | semidirect |
| 3. #22577644 | C2 | semidirect |
| 4. #22577230 | C2 | semidirect |
| 5. #22577206 | C2 | semidirect |
| 6. #22577204 | C2 | semidirect |
| 28. #14555485 | D4 | semidirect |
| 62. C22×C137 | SD32 | semidirect |
| 75. C137 | #2217 | semidirect |
| 138. C22 | #17984032 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984032 | 2 |
| C22×#14555485 | 2 |
| #22577644 | 2 |
| #22577230 | 2 |
| #22577206 | 2 |
| #22577204 | 2 |
| #466×C137 | 2 |
| #2217 | 137 |