Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
164 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 51 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×#17984033 | C2 | semidirect |
| 2. C2×C16×D137 | C2 | semidirect |
| 3. #22577645 | C2 | semidirect |
| 5. #22577206 | C2 | semidirect |
| 6. #22577203 | C2 | semidirect |
| 7. #367×C137 | C2 | semidirect |
| 39. C16×C137 | D4 | semidirect |
| 63. C2×D137 | SD32 | semidirect |
| 75. C137 | #2217 | semidirect |
| 81. #367 | D137 | semidirect |
| 115. C16 | D548 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984033 | 2 |
| C2×C16×D137 | 2 |
| #22577645 | 2 |
| #22577640 | 2 |
| #22577206 | 2 |
| #22577203 | 2 |
| #367×C137 | 2 |
| #2217 | 137 |