Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
398 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 5. #10593534 | C2 | direct (N × H) |
| 86. C2×C32 | #499 | semidirect |
| 88. C3⋊D3 | #499 | semidirect |
| 113. C32 | C2×#499 | semidirect |
| 145. C2 | #10593534 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64243 | 2 |
| C2×#63769 | 2 |
| C2×C8×#157 | 2 |
| C2×#63745 | 2 |
| #10593534 | 2 |
| C2×#499 | 9 |