Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
717 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 717 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 1. C2×C9×AGL(1,ℤ/8) | C2 | semidirect |
| 2. #10589932 | C2 | semidirect |
| 3. C2×#63502 | C2 | semidirect |
| 4. C2×#63396 | C2 | semidirect |
| 5. #10588896 | C2 | semidirect |
| 6. C2×#63383 | C2 | semidirect |
| 7. #10588235 | C2 | semidirect |
| 43. C2×Q8×C9 | D4 | semidirect |
| 50. C2×D4×C9 | D4 | semidirect |
| 51. C2×D4×C9 | D4 | semidirect |
| 67. C9×M16 | D4 | semidirect |
| 71. C4⋊Dic9 | D4 | semidirect |
| 74. C4×Dic9 | D4 | semidirect |
| 140. C2×AGL(1,ℤ/8) | D9 | semidirect |
| 283. C2×Q8 | #611 | semidirect |
| 299. C2×D4 | #611 | semidirect |
| 300. C2×D4 | #611 | semidirect |
| 309. M16 | #611 | semidirect |
| 339. C9 | #2002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×AGL(1,ℤ/8) | 2 |
| #10589932 | 2 |
| C2×#63502 | 2 |
| C2×#63396 | 2 |
| #10588896 | 2 |
| C2×#63383 | 2 |
| #10588235 | 2 |
| #72094 | 3 |