Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
174 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 81 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×C16×D137 | C2 | semidirect |
| 3. #22577221 | C2 | semidirect |
| 4. C22⋊#14555485 | C2 | semidirect |
| 5. #22577182 | C2 | semidirect |
| 6. C16×Dic137 | C2 | semidirect |
| 7. C22×C16×C137 | C2 | semidirect |
| 39. C16×C137 | D4 | semidirect |
| 41. C22⋊D137 | C16 | direct (N × H) |
| 59. C22×C137 | C2×C16 | semidirect |
| 63. C2×D137 | C2×C16 | semidirect |
| 69. Dic137 | C2×C16 | semidirect |
| 75. C137 | D4×C16 | semidirect |
| 78. C22×C16 | D137 | semidirect |
| 115. C16 | C22⋊D137 | direct (N × H) |
| 138. C22 | C16×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C16×D137 | 2 |
| C8×C22⋊D137 | 2 |
| #22577221 | 2 |
| C22⋊#14555485 | 2 |
| #22577182 | 2 |
| C16×Dic137 | 2 |
| C22×C16×C137 | 2 |
| D4×C16 | 137 |