Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
552 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 194 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. C22×#14555519 | C2 | semidirect |
| 2. #22578438 | C2 | direct (N × H) |
| 3. C2×C4⋊#11764047 | C2 | semidirect |
| 4. C2×C22⋊#11764047 | C2 | semidirect |
| 5. C2×C4×#11764047 | C2 | semidirect |
| 8. C2×#14555519 | C22 | semidirect |
| 12. C4⋊#11764047 | C22 | semidirect |
| 13. C22⋊#11764047 | C22 | semidirect |
| 14. C4×#11764047 | C22 | semidirect |
| 25. C2×#11764047 | D4 | semidirect |
| 46. #11764047 | C2×D4 | semidirect |
| 64. C2×C4×C137 | M16 | semidirect |
| 74. C4×C137 | C2×M16 | semidirect |
| 81. C2×C137 | #436 | semidirect |
| 85. C137 | C2×#436 | semidirect |
| 147. C2×C4 | #14555519 | semidirect |
| 165. C4 | C2×#14555519 | semidirect |
| 167. C2 | #22578438 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555519 | 2 |
| #22578438 | 2 |
| C2×C4⋊#11764047 | 2 |
| C2×C22⋊#11764047 | 2 |
| C2×C4×#11764047 | 2 |
| C2×D4×Dic137 | 2 |
| C2×#436 | 137 |