Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
385 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 385 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 96. C32×C8 | Q16 | semidirect |
| 191. C3×C8 | #216 | semidirect |
| 192. C3×C8 | #216 | semidirect |
| 239. C32 | #1723 | semidirect |
| 253. C8 | #3718 | semidirect |
| 272. C3 | #71341 | semidirect |
| 273. C3 | #71367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4682 | 2 |
| C3×#4680 | 2 |
| #10590387 | 2 |
| #10590312 | 2 |
| #10590290 | 2 |
| #10589321 | 2 |
| #71367 | 3 |
| #71341 | 3 |