Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
210 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 80 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 | #127 |
| commutator, Frattini, cosocle | C22×C4 | C23×C23 |
| socle | C2×C23 | #399 |
| prime radical | C2×#41×C23 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C23 ◁ C22×C4×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#430 | C2 | semidirect |
| 2. C23×#424 | C2 | semidirect |
| 5. C23×H(3,ℤ/4) | C2 | semidirect |
| 48. #2098 | C23 | direct (N × H) |
| 59. #430 | C2×C23 | semidirect |
| 60. #424 | C2×C23 | semidirect |
| 63. H(3,ℤ/4) | C2×C23 | semidirect |
| 77. C23 | #2098 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#430 | 2 |
| C23×#424 | 2 |
| C23×#421 | 2 |
| C23×#408 | 2 |
| C23×H(3,ℤ/4) | 2 |
| #2098 | 23 |