Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
174 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 77 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×#14555522 | C2 | semidirect |
| 2. C4⋊#14555522 | C2 | semidirect |
| 3. C22⋊#14555522 | C2 | semidirect |
| 4. C4×#14555522 | C2 | semidirect |
| 17. #14555522 | D4 | direct (N × H) |
| 38. D4×C137 | C16 | semidirect |
| 42. C22×C137 | C2×C16 | semidirect |
| 44. C4×C137 | C2×C16 | semidirect |
| 53. C137 | D4×C16 | semidirect |
| 83. D4 | #14555522 | direct (N × H) |
| 96. C22 | C2×#14555522 | semidirect |
| 102. C4 | C2×#14555522 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555522 | 2 |
| C4⋊#14555522 | 2 |
| C22⋊#14555522 | 2 |
| C4×#14555522 | 2 |
| D4×#11764047 | 2 |
| D4×C16 | 137 |