Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
604 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 237 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 |
|---|---|---|
| 2. #22577341 | C2 | direct (N × H) |
| 77. C2×C137 | #400 | semidirect |
| 83. C137 | C2×#400 | semidirect |
| 161. C2 | #22577341 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555489 | 2 |
| #22577341 | 2 |
| C2×#17983995 | 2 |
| C22×C4⋊C4×C137 | 2 |
| C2×#400 | 137 |