Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
1048 conjugacy classes of subgroups.
The subgroup lattice has 128 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C23 | C24 |
| commutator, Frattini, cosocle | C22 | C25×C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#557 | C2 | direct (N × H) |
| 22. C2×Q8×C23 | Q8 | semidirect |
| 39. Q8×C23 | C2×Q8 | semidirect |
| 50. C2×#557 | C23 | direct (N × H) |
| 60. #557 | C2×C23 | direct (N × H) |
| 66. C2×C23 | #557 | direct (N × H) |
| 84. C23 | C2×#557 | direct (N × H) |
| 86. C2×Q8 | Q8×C23 | semidirect |
| 103. Q8 | C2×Q8×C23 | semidirect |
| 123. C2 | C23×#557 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#557 | 2 |
| C2×C23×C4⋊Q8 | 2 |
| C2×C23×#125 | 2 |
| C2×C4×Q8×C23 | 2 |
| C2×#557 | 23 |