Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
260 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | C2×D8 |
| commutator | C8 | C22×C4×C23 |
| Frattini, cosocle | C2×C8 | C23×C23 |
| prime radical | C22×D8×C23 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×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×#427 | C2 | semidirect |
| 4. C23×#357 | C2 | semidirect |
| 8. C2×D8×C23 | C4 | semidirect |
| 13. C2×C16×C23 | C22 | semidirect |
| 14. C23×#107 | C22 | semidirect |
| 48. #2140 | C23 | direct (N × H) |
| 60. C2×M32 | C2×C23 | semidirect |
| 61. #427 | C2×C23 | semidirect |
| 62. #357 | C2×C23 | semidirect |
| 70. C2×D8 | C4×C23 | semidirect |
| 75. C2×C16 | C22×C23 | semidirect |
| 76. #107 | C22×C23 | semidirect |
| 78. C23 | #2140 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D8×C23 | 2 |
| C2×C23×M32 | 2 |
| C23×#427 | 2 |
| C23×#357 | 2 |
| #2140 | 23 |