Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
388 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C23 | C22⋊C4 |
| commutator | C22 | C2×C42×C23 |
| Frattini, cosocle | C22×C4 | C23×C23 |
| socle | C22×C23 | C2×C22⋊C4 |
| prime radical | C24×C23 | C2×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C23 ◁ C23×C4×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C23×#343 | C2 | semidirect |
| 7. C2×M16×C23 | C4 | semidirect |
| 53. #1742 | C23 | direct (N × H) |
| 69. #343 | C2×C23 | semidirect |
| 78. C2×M16 | C4×C23 | semidirect |
| 86. C23 | #1742 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×M16×C23 | 2 |
| C2×C23×#117 | 2 |
| C23×#343 | 2 |
| #1742 | 23 |