Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
632 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 171 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×C52×Q8 | C2 | semidirect |
| 2. C2×#87811 | C2 | semidirect |
| 4. #11716702 | C2 | semidirect |
| 5. C22⋊#6029 | C2 | semidirect |
| 22. C52×Q8 | D4 | semidirect |
| 32. C22×C5×Q8 | D5 | semidirect |
| 39. C22×C52 | SD16 | semidirect |
| 69. C5×Q8 | C22⋊D5 | semidirect |
| 79. C22×Q8 | C5⋊D5 | semidirect |
| 84. C52 | #448 | semidirect |
| 87. C22×C5 | #688 | semidirect |
| 116. Q8 | C22⋊(C5⋊D5) | semidirect |
| 126. C5 | #65516 | semidirect |
| 132. C22 | #87811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×Q8 | 2 |
| C2×#87811 | 2 |
| #11717250 | 2 |
| #11716702 | 2 |
| C22⋊#6029 | 2 |
| #65516 | 5 |