Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
358 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C23 | C2×D4 |
| commutator | C2×C4 | C22×C4×C23 |
| Frattini, cosocle | C22×C4 | C23×C23 |
| socle | C22×C23 | C2×C22⋊C4 |
| prime radical | C23×#525 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C23 ◁ C23×C4×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C23×#117 | C2 | semidirect |
| 3. C2×C23×#104 | C2 | semidirect |
| 4. C23×#407 | C2 | semidirect |
| 5. C23×#339 | C2 | semidirect |
| 10. C23×C22⋊Q8 | C4 | semidirect |
| 11. C23×#121 | C4 | semidirect |
| 48. C42×C23 | D4 | semidirect |
| 75. #1897 | C23 | direct (N × H) |
| 94. C2×#117 | C2×C23 | semidirect |
| 95. C2×#104 | C2×C23 | semidirect |
| 96. #407 | C2×C23 | semidirect |
| 97. #339 | C2×C23 | semidirect |
| 108. C22⋊Q8 | C4×C23 | semidirect |
| 109. #121 | C4×C23 | semidirect |
| 119. C23 | #1897 | direct (N × H) |
| 147. C42 | D4×C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#525 | 2 |
| C2×C23×#117 | 2 |
| C2×C23×#104 | 2 |
| C23×#407 | 2 |
| C23×#339 | 2 |
| #1897 | 23 |