Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
528 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 157 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. #10592387 | C2 | semidirect |
| 3. C32×#322 | C2 | semidirect |
| 4. #10589325 | C2 | semidirect |
| 5. #10589323 | C2 | semidirect |
| 19. C3×#322 | D3 | semidirect |
| 57. C32×C8 | M16 | semidirect |
| 63. #322 | C3⋊D3 | semidirect |
| 107. C3×C8 | ΓL(1,𝔽25) | semidirect |
| 134. C32 | #1594 | semidirect |
| 148. C8 | #3743 | semidirect |
| 162. C3 | #68083 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3745 | 2 |
| #10592387 | 2 |
| C32×#322 | 2 |
| #10589325 | 2 |
| #10589323 | 2 |
| #68083 | 3 |