Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
272 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 89 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×#17984183 | C2 | semidirect |
| 2. #22578500 | C2 | semidirect |
| 3. C22⋊#14555522 | C2 | semidirect |
| 6. C2×#14555522 | C22 | semidirect |
| 41. C22×D137 | C16 | semidirect |
| 60. C22×C137 | C2×C16 | semidirect |
| 67. C2×D137 | C2×C16 | semidirect |
| 79. D137 | C22⋊C16 | semidirect |
| 80. C137 | C2×C22⋊C16 | semidirect |
| 148. C22 | #17984183 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984183 | 2 |
| #22578500 | 2 |
| C22⋊#14555522 | 2 |
| C22×#14555518 | 2 |
| C2×C22⋊C16 | 137 |