Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
500 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 170 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×#17984175 | C2 | semidirect |
| 2. #22578438 | C2 | semidirect |
| 3. D4×#11764047 | C2 | semidirect |
| 4. #22578407 | C2 | semidirect |
| 5. #22578377 | C2 | semidirect |
| 6. C4×#14555518 | C2 | semidirect |
| 28. #14555518 | D4 | semidirect |
| 74. C4×C137 | #131 | semidirect |
| 83. C137 | #2931 | semidirect |
| 162. C4 | #17984175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984175 | 2 |
| #22578438 | 2 |
| D4×#11764047 | 2 |
| #22578407 | 2 |
| #22578377 | 2 |
| C4×#14555518 | 2 |
| #22577951 | 2 |
| #2931 | 137 |