Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
144 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C23 | #106 |
| commutator | C8 | C22×C4×C23 |
| Frattini, cosocle | C2×C8 | C23×C23 |
| socle | C2×C23 | C2×#106 |
| prime radical | C23×C23 | SD16 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C23 ◁ C22×C4×C23 ◁ C22×C8×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C23×#365 | C2 | semidirect |
| 8. C23×M32 | C4 | semidirect |
| 10. C2×C16×C23 | C4 | semidirect |
| 42. #2155 | C23 | direct (N × H) |
| 55. #365 | C2×C23 | semidirect |
| 63. M32 | C4×C23 | semidirect |
| 65. C2×C16 | C4×C23 | semidirect |
| 70. C23 | #2155 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C23×M32 | 2 |
| C2×C23×#108 | 2 |
| C23×#427 | 2 |
| C23×#365 | 2 |
| #2155 | 23 |