Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
348 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 88 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 | #392 |
| commutator, Frattini, cosocle | C22×C4 | C23×C23 |
| prime radical | C23×#575 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C22×C4×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C23×#137 | C2 | semidirect |
| 3. C23×#536 | C2 | semidirect |
| 4. C23×#421 | C2 | semidirect |
| 5. C23×#419 | C2 | semidirect |
| 6. C23×#410 | C2 | semidirect |
| 7. C23×#344 | C2 | semidirect |
| 113. #2009 | C23 | direct (N × H) |
| 132. C2×#137 | C2×C23 | semidirect |
| 133. #536 | C2×C23 | semidirect |
| 134. #421 | C2×C23 | semidirect |
| 135. #419 | C2×C23 | semidirect |
| 136. #410 | C2×C23 | semidirect |
| 137. #344 | C2×C23 | semidirect |
| 167. C23 | #2009 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#575 | 2 |
| C2×C23×#137 | 2 |
| C23×#536 | 2 |
| C23×#421 | 2 |
| C23×#419 | 2 |
| C23×#410 | 2 |
| C23×#344 | 2 |
| #2009 | 23 |