Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
930 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 182 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. #10588916 | C2 | semidirect |
| 3. C2×#63396 | C2 | semidirect |
| 4. #10588901 | C2 | semidirect |
| 5. C2×#63391 | C2 | semidirect |
| 9. C9×H(5,𝔽2) | C4 | semidirect |
| 16. C2×C4⋊Dic9 | C22 | semidirect |
| 17. C2×C4×Dic9 | C22 | semidirect |
| 18. C2×#3667 | C22 | semidirect |
| 87. Q8×C9 | C22⋊C4 | semidirect |
| 94. D4×C9 | C22⋊C4 | semidirect |
| 166. H(5,𝔽2) | Dic9 | semidirect |
| 270. C9 | #1792 | semidirect |
| 282. Q8 | #3676 | semidirect |
| 289. D4 | #3676 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×H(5,𝔽2) | 2 |
| #10588916 | 2 |
| C2×#63396 | 2 |
| #10588901 | 2 |
| C2×#63391 | 2 |
| #72140 | 3 |