Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
1376 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 1376 conjugacy classes of subgroups — too many to draw. Only its 202 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 |
|---|---|---|
| 2. #13104690 | C2 | semidirect |
| 3. C4×#87855 | C2 | semidirect |
| 4. D4⋊#6033 | C2 | semidirect |
| 5. #13100249 | C2 | semidirect |
| 20. C4⋊#6033 | C22 | semidirect |
| 22. C4×#6033 | C22 | semidirect |
| 30. D4×C5⋊D5 | C8 | semidirect |
| 67. C52×D4 | C2×C8 | semidirect |
| 81. C4⋊(C5⋊D5) | C2×C8 | semidirect |
| 173. C5⋊D5 | D4⋊C8 | semidirect |
| 181. C5×D4 | D5⋊C8 | semidirect |
| 224. C52 | C2×D4⋊C8 | semidirect |
| 293. D4 | #87855 | semidirect |
| 316. C5 | D5⋊(D4⋊C8) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×C5⋊D5 | 2 |
| #13104690 | 2 |
| C4×#87855 | 2 |
| D4⋊#6033 | 2 |
| #13100249 | 2 |
| D5⋊(D4⋊C8) | 5 |