Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
388 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 164 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. #22578454 | C2 | semidirect |
| 2. #22578438 | C2 | semidirect |
| 3. #22578434 | C2 | semidirect |
| 4. #22578424 | C2 | semidirect |
| 5. #22578419 | C2 | semidirect |
| 6. #22578406 | C2 | semidirect |
| 7. C2×C4⋊#11764047 | C2 | semidirect |
| 81. C2×C4×C137 | M16 | semidirect |
| 107. C137 | #2989 | semidirect |
| 186. C2×C4 | #14555519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578454 | 2 |
| #22578438 | 2 |
| #22578434 | 2 |
| #22578424 | 2 |
| #22578419 | 2 |
| #22578406 | 2 |
| C2×C4⋊#11764047 | 2 |
| #41×Dic137 | 2 |
| #2989 | 137 |