Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
536 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 178 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×#6033 | C2 | semidirect |
| 3. C22⋊#6033 | C2 | semidirect |
| 4. C4⋊#6033 | C2 | semidirect |
| 5. C4×#6033 | C2 | semidirect |
| 17. C52×D4 | C8 | semidirect |
| 26. #6033 | D4 | direct (N × H) |
| 34. C22×C52 | C2×C8 | semidirect |
| 36. C4×C52 | C2×C8 | semidirect |
| 56. C5×D4 | #170 | semidirect |
| 71. C52 | C8×D4 | semidirect |
| 74. C22×C5 | C2×#170 | semidirect |
| 76. C4×C5 | C2×#170 | semidirect |
| 95. D4 | #6033 | direct (N × H) |
| 105. C5 | D4×#170 | semidirect |
| 108. C22 | C2×#6033 | semidirect |
| 114. C4 | C2×#6033 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6033 | 2 |
| D4×#1039 | 2 |
| C22⋊#6033 | 2 |
| C4⋊#6033 | 2 |
| C4×#6033 | 2 |
| D4×#170 | 5 |