Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
371 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 371 conjugacy classes of subgroups — too many to draw. Only its 86 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. C4×#3746 | C2 | semidirect |
| 3. C2×#63551 | C2 | semidirect |
| 5. C3×C4⋊(C3⋊C16) | C2 | semidirect |
| 6. #10589118 | C2 | semidirect |
| 37. C4⋊(C3⋊C16) | D3 | semidirect |
| 281. C32 | #2211 | semidirect |
| 321. C3 | #69294 | semidirect |
| 322. C3 | #71324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3746 | 2 |
| C3×#4696 | 2 |
| C2×#63551 | 2 |
| C2×#63548 | 2 |
| C3×C4⋊(C3⋊C16) | 2 |
| #10589118 | 2 |
| #10589115 | 2 |
| #71324 | 3 |
| #69294 | 3 |