Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1074 conjugacy classes of subgroups; only the 250 normal subgroups are shown.
This group has 1074 conjugacy classes of subgroups — too many to draw. Only its 250 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 |
|---|---|---|
| 3. C2×C4⋊#622 | C2 | semidirect |
| 4. #10593728 | C2 | direct (N × H) |
| 15. C4⋊#622 | C22 | semidirect |
| 48. C2×C32×C4 | M16 | semidirect |
| 88. C32×C4 | C2×M16 | semidirect |
| 122. C2×C32 | #423 | semidirect |
| 156. C32 | C2×#423 | semidirect |
| 171. C2×C4 | #3788 | semidirect |
| 190. C4 | C2×#3788 | semidirect |
| 194. C2 | #10593728 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3788 | 2 |
| C2×C42×C3⋊D3 | 2 |
| C2×C4⋊#622 | 2 |
| #10593728 | 2 |
| C2×#423 | 9 |