Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1341 conjugacy classes of subgroups; only the 220 normal subgroups are shown.
This group has 1341 conjugacy classes of subgroups — too many to draw. Only its 220 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. C22×#3743 | C2 | semidirect |
| 2. C2×#63916 | C2 | semidirect |
| 3. C22×#3713 | C2 | semidirect |
| 4. C2×C3×#821 | C2 | semidirect |
| 5. C2×#63574 | C2 | semidirect |
| 6. #10590840 | C2 | direct (N × H) |
| 14. C2×#3743 | C22 | semidirect |
| 18. #63916 | C22 | semidirect |
| 20. C2×#3713 | C22 | semidirect |
| 21. C3×#821 | C22 | semidirect |
| 22. #63574 | C22 | semidirect |
| 29. C2×#821 | D3 | semidirect |
| 49. C2×C3⋊(C3⋊C8) | D4 | semidirect |
| 82. #821 | C2×D3 | semidirect |
| 108. C3⋊(C3⋊C8) | C2×D4 | semidirect |
| 243. C2×C32 | #469 | semidirect |
| 304. C32 | C2×#469 | semidirect |
| 334. C2×C3 | #4782 | semidirect |
| 357. C3 | C2×#4782 | semidirect |
| 360. C2 | #10590840 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3743 | 2 |
| C2×#63916 | 2 |
| C22×#3713 | 2 |
| C2×C3×#821 | 2 |
| C2×#63574 | 2 |
| #10590840 | 2 |
| C2×#4782 | 3 |