Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
560 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 280 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 | C22 | C23×C4×C23 |
| Frattini, cosocle | C23 | C24×C23 |
| prime radical | C22×D4×C23 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#391 | C2 | semidirect |
| 3. C23×#388 | C2 | semidirect |
| 5. C4×C22⋊C4×C23 | C2 | semidirect |
| 6. C23×#376 | C2 | semidirect |
| 10. C23×#124 | C4 | semidirect |
| 25. C2×Q8×C23 | C2×C4 | semidirect |
| 39. C22⋊C4×C23 | C2×C4 | semidirect |
| 42. C42×C23 | C2×C4 | semidirect |
| 66. #2372 | C23 | direct (N × H) |
| 82. #391 | C2×C23 | semidirect |
| 83. #388 | C2×C23 | semidirect |
| 85. C4×C22⋊C4 | C2×C23 | semidirect |
| 86. #376 | C2×C23 | semidirect |
| 95. #124 | C4×C23 | semidirect |
| 107. C23 | #2372 | direct (N × H) |
| 111. C2×Q8 | C2×C4×C23 | semidirect |
| 125. C22⋊C4 | C2×C4×C23 | semidirect |
| 128. C42 | C2×C4×C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C23×#124 | 2 |
| C23×#391 | 2 |
| C23×#388 | 2 |
| C23×#386 | 2 |
| C4×C22⋊C4×C23 | 2 |
| C23×#376 | 2 |
| #2372 | 23 |