Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
581 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 581 conjugacy classes of subgroups — too many to draw. Only its 96 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×#3746 | C2 | semidirect |
| 3. C2×#63548 | C2 | semidirect |
| 4. C3×#4549 | C2 | semidirect |
| 5. #10589119 | C2 | semidirect |
| 27. #4549 | D3 | semidirect |
| 43. #3746 | D4 | semidirect |
| 148. C22×C32 | SD32 | semidirect |
| 249. C22×C3 | #800 | semidirect |
| 250. C22×C3 | #827 | semidirect |
| 270. C32 | #2185 | semidirect |
| 307. C22 | #63548 | semidirect |
| 315. C3 | #69112 | semidirect |
| 316. C3 | #71077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3746 | 2 |
| C3×#5115 | 2 |
| C2×#63548 | 2 |
| C3×#4549 | 2 |
| #10589119 | 2 |
| #71077 | 3 |
| #69112 | 3 |