Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
1072 conjugacy classes of subgroups; only the 378 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 378 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. C23×#11764047 | C2 | semidirect |
| 2. C2×C22⋊#11764047 | C2 | direct (N × H) |
| 5. C22×#11764047 | C22 | semidirect |
| 6. C22⋊#11764047 | C22 | direct (N × H) |
| 14. C2×#11764047 | C23 | semidirect |
| 26. C24×C137 | C8 | semidirect |
| 43. C23×C137 | C2×C8 | semidirect |
| 50. C22×C137 | C22⋊C8 | semidirect |
| 53. C22×C137 | C22×C8 | semidirect |
| 60. C2×C137 | C2×C22⋊C8 | semidirect |
| 64. C137 | C22×C22⋊C8 | semidirect |
| 80. C24 | #11764047 | semidirect |
| 99. C23 | C2×#11764047 | semidirect |
| 115. C22 | C22⋊#11764047 | direct (N × H) |
| 118. C22 | C22×#11764047 | semidirect |
| 125. C2 | C2×C22⋊#11764047 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11764047 | 2 |
| C2×C22⋊#11764047 | 2 |
| C24×Dic137 | 2 |
| C22×C22⋊C8 | 137 |