Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
399 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 399 conjugacy classes of subgroups — too many to draw. Only its 110 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. C4×C9×M16 | C2 | semidirect |
| 3. #10588604 | C2 | semidirect |
| 4. #10588136 | C2 | semidirect |
| 5. #10588133 | C2 | semidirect |
| 94. D36 | M16 | semidirect |
| 100. Dic18 | M16 | semidirect |
| 105. C4×M16 | D9 | semidirect |
| 251. C9 | #1489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3697 | 2 |
| C4×C9×M16 | 2 |
| #10588604 | 2 |
| #10588136 | 2 |
| #10588133 | 2 |
| #69854 | 3 |