Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
544 conjugacy classes of subgroups; only the 248 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 248 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C23 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C23 |
| prime radical | C24×C23 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C23×#398 | C2 | semidirect |
| 4. C23×#391 | C2 | semidirect |
| 6. C23×#384 | C2 | semidirect |
| 42. C22⋊C4×C23 | Q8 | semidirect |
| 65. #2502 | C23 | direct (N × H) |
| 82. #398 | C2×C23 | semidirect |
| 83. #391 | C2×C23 | semidirect |
| 85. #384 | C2×C23 | semidirect |
| 107. C23 | #2502 | direct (N × H) |
| 127. C22⋊C4 | Q8×C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C23×C22⋊Q8 | 2 |
| C22×C4⋊C4×C23 | 2 |
| C23×#398 | 2 |
| C23×#391 | 2 |
| C23×#385 | 2 |
| C23×#384 | 2 |
| C4×C22⋊C4×C23 | 2 |
| #2502 | 23 |