Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
226 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C23 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C23×C23 |
| prime radical | C23×H(5,𝔽2) | C22 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C22×C23 ◁ C2×D4×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#563 | C2 | semidirect |
| 4. C23×#354 | C2 | semidirect |
| 5. C23×#352 | C2 | semidirect |
| 62. #2201 | C23 | direct (N × H) |
| 75. #563 | C2×C23 | semidirect |
| 78. #354 | C2×C23 | semidirect |
| 79. #352 | C2×C23 | semidirect |
| 97. C23 | #2201 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#563 | 2 |
| C23×#458 | 2 |
| C23×#455 | 2 |
| C23×#354 | 2 |
| C23×#352 | 2 |
| #2201 | 23 |