Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
336 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 116 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×#532 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C23 ◁ C2×C42×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C23×#104 | C2 | semidirect |
| 3. C4×M16×C23 | C2 | semidirect |
| 4. C4×C4⋊C4×C23 | C2 | semidirect |
| 7. C23×C4⋊Q8 | C4 | semidirect |
| 8. C23×#127 | C4 | semidirect |
| 9. C23×#124 | C4 | semidirect |
| 34. M16×C23 | D4 | semidirect |
| 70. #1980 | C23 | direct (N × H) |
| 84. C4×C23 | #104 | semidirect |
| 88. C2×#104 | C2×C23 | semidirect |
| 89. C4×M16 | C2×C23 | semidirect |
| 90. C4×C4⋊C4 | C2×C23 | semidirect |
| 99. C4⋊Q8 | C4×C23 | semidirect |
| 100. #127 | C4×C23 | semidirect |
| 101. #124 | C4×C23 | semidirect |
| 113. C23 | #1980 | direct (N × H) |
| 127. M16 | D4×C23 | semidirect |
| 176. C4 | C23×#104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#532 | 2 |
| C2×C23×#104 | 2 |
| C4×M16×C23 | 2 |
| C4×C4⋊C4×C23 | 2 |
| #1980 | 23 |