Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
309 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 309 conjugacy classes of subgroups — too many to draw. Only its 62 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. C9×#510 | C2 | semidirect |
| 3. #10588872 | C2 | semidirect |
| 4. C2×#63388 | C2 | semidirect |
| 5. #10588244 | C2 | semidirect |
| 6. #10588195 | C2 | semidirect |
| 7. #10588192 | C2 | semidirect |
| 102. #510 | D9 | semidirect |
| 224. C9 | #2195 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589873 | 2 |
| C9×#510 | 2 |
| #10588872 | 2 |
| C2×#63388 | 2 |
| #10588244 | 2 |
| #10588195 | 2 |
| #10588192 | 2 |
| #71524 | 3 |