Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
384 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#17984021 | C2 | semidirect |
| 3. C2×#17984009 | C2 | semidirect |
| 4. C2×#17984008 | C2 | semidirect |
| 5. C2×C4×#11764040 | C2 | semidirect |
| 6. #22577305 | C2 | semidirect |
| 7. #390×C137 | C2 | semidirect |
| 11. C2×#14555495 | C4 | semidirect |
| 69. #11764040 | C22⋊C4 | semidirect |
| 84. C2×C4×C137 | D8 | semidirect |
| 120. C137 | #1970 | semidirect |
| 128. #390 | D137 | semidirect |
| 203. C2×C4 | #14555495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555495 | 2 |
| C2×#17984021 | 2 |
| C2×#17984009 | 2 |
| C2×#17984008 | 2 |
| C2×C4×#11764040 | 2 |
| #22577305 | 2 |
| #390×C137 | 2 |
| #1970 | 137 |