Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
228 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | AΣL(1,𝔽16) |
| commutator | C2×C4⋊C4 | C2×C4×C23 |
| Frattini, cosocle | #384 | C22×C23 |
| prime radical | C23×#537 | C4 |
| LCS | G ▷ C2×C4⋊C4 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C23×C23 ◁ C22×C4×C23 ◁ C23×#384 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#1325 | C2 | semidirect |
| 3. C23×#1296 | C2 | semidirect |
| 57. #7417 | C23 | direct (N × H) |
| 88. #1325 | C2×C23 | semidirect |
| 89. #1296 | C2×C23 | semidirect |
| 137. C23 | #7417 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2039 | 2 |
| C23×#1325 | 2 |
| C23×#1296 | 2 |
| #7417 | 23 |