Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
266 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 84 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 | C2×#99 |
| commutator | C23 | C22×C4×C23 |
| Frattini, cosocle | C2×D4 | C23×C23 |
| prime radical | C23×#535 | C2 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C2×C4×C23 ◁ C2×#41×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#413 | C2 | semidirect |
| 3. C23×#410 | C2 | semidirect |
| 4. C23×AΣL(1,𝔽16) | C2 | semidirect |
| 6. C22×D4×C23 | C4 | semidirect |
| 12. C23×#120 | C4 | semidirect |
| 15. C23×#117 | C4 | semidirect |
| 75. #2122 | C23 | direct (N × H) |
| 95. #413 | C2×C23 | semidirect |
| 96. #410 | C2×C23 | semidirect |
| 97. AΣL(1,𝔽16) | C2×C23 | semidirect |
| 105. C22×D4 | C4×C23 | semidirect |
| 111. #120 | C4×C23 | semidirect |
| 114. #117 | C4×C23 | semidirect |
| 119. C23 | #2122 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#535 | 2 |
| C23×#413 | 2 |
| C23×#410 | 2 |
| C23×AΣL(1,𝔽16) | 2 |
| #2122 | 23 |