Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
286 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 92 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×C22⋊C4 |
| commutator | C2×C4 | C22×C4×C23 |
| Frattini, cosocle | C22×C4 | C23×C23 |
| prime radical | C23×#525 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C23×C4×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#407 | C2 | semidirect |
| 3. C23×#380 | C2 | semidirect |
| 4. C23×#328 | C2 | semidirect |
| 5. C23×#327 | C2 | semidirect |
| 6. C2×#41×C23 | C4 | semidirect |
| 10. C23×C22⋊Q8 | C4 | semidirect |
| 12. C23×#121 | C4 | semidirect |
| 17. C23×#117 | C4 | semidirect |
| 85. #1513 | C23 | direct (N × H) |
| 111. #407 | C2×C23 | semidirect |
| 112. #380 | C2×C23 | semidirect |
| 113. #328 | C2×C23 | semidirect |
| 114. #327 | C2×C23 | semidirect |
| 123. C2×#41 | C4×C23 | semidirect |
| 127. C22⋊Q8 | C4×C23 | semidirect |
| 129. #121 | C4×C23 | semidirect |
| 134. #117 | C4×C23 | semidirect |
| 140. C23 | #1513 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#525 | 2 |
| C23×#407 | 2 |
| C23×#380 | 2 |
| C23×#328 | 2 |
| C23×#327 | 2 |
| #1513 | 23 |