Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
1168 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 150 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 | C2×#99 |
| commutator | C24 | C22×C4×C23 |
| Frattini, cosocle | C22×D4 | C23×C23 |
| prime radical | C2×C23×#535 | C2 |
| LCS | G ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×C4×C23 ◁ C22×#41×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C23×AΣL(1,𝔽16) | C2 | semidirect |
| 3. C23×#1785 | C2 | semidirect |
| 4. C23×#1782 | C2 | semidirect |
| 6. C23×D4×C23 | C4 | semidirect |
| 12. C2×C23×#120 | C4 | semidirect |
| 14. C2×C23×#117 | C4 | semidirect |
| 121. #12691 | C23 | direct (N × H) |
| 175. C2×AΣL(1,𝔽16) | C2×C23 | semidirect |
| 176. #1785 | C2×C23 | semidirect |
| 177. #1782 | C2×C23 | semidirect |
| 208. C23×D4 | C4×C23 | semidirect |
| 214. C2×#120 | C4×C23 | semidirect |
| 216. C2×#117 | C4×C23 | semidirect |
| 272. C23 | #12691 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C23×#535 | 2 |
| C2×C23×AΣL(1,𝔽16) | 2 |
| C23×#1785 | 2 |
| C23×#1782 | 2 |
| #12691 | 23 |