Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
648 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 137 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. #10592894 | C2 | semidirect |
| 3. #10592836 | C2 | semidirect |
| 4. #10589432 | C2 | semidirect |
| 5. #10589419 | C2 | semidirect |
| 14. C2×#3746 | C22 | semidirect |
| 17. #63644 | C22 | semidirect |
| 19. #63639 | C22 | semidirect |
| 197. C32 | #2191 | semidirect |
| 234. C3 | #72113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#575 | 2 |
| #10592894 | 2 |
| #10592836 | 2 |
| #10589432 | 2 |
| #10589419 | 2 |
| #72113 | 3 |