Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
420 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 172. C32 | #1696 | semidirect |
| 202. C3 | #71153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#477 | 2 |
| #10592777 | 2 |
| #10592723 | 2 |
| #10592720 | 2 |
| #10589412 | 2 |
| #10589347 | 2 |
| #10589346 | 2 |
| #71153 | 3 |