Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
236 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 120 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 | C22×C8×C23 |
| Frattini, cosocle | C2×C8 | C23×C23 |
| socle | C22×C23 | C22⋊C8 |
| prime radical | C24×C23 | C8 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C23 ◁ C22×C8×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C23×M32 | C2 | semidirect |
| 3. C23×#349 | C2 | direct (N × H) |
| 12. C23×M32 | C22 | semidirect |
| 54. C2×#349 | C23 | direct (N × H) |
| 69. C2×M32 | C2×C23 | semidirect |
| 70. #349 | C2×C23 | direct (N × H) |
| 74. C2×C23 | #349 | direct (N × H) |
| 84. M32 | C22×C23 | semidirect |
| 86. C23 | C2×#349 | direct (N × H) |
| 143. C2 | C23×#349 | 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×M32 | 2 |
| C23×#349 | 2 |
| C2×#349 | 23 |