Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
348 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 181 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. #22577532 | C2 | semidirect |
| 3. #22577530 | C2 | semidirect |
| 33. C2×#11764040 | Q8 | semidirect |
| 83. C137 | #2961 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577956 | 2 |
| #22577532 | 2 |
| #22577530 | 2 |
| #22577429 | 2 |
| #22577426 | 2 |
| #22577361 | 2 |
| #22577359 | 2 |
| C2×#17983998 | 2 |
| #424×C137 | 2 |
| #2961 | 137 |