Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
816 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 158 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C23 | #120 |
| commutator | C42 | C22×C4×C23 |
| Frattini, cosocle | C2×C42 | C23×C23 |
| prime radical | C2×C23×#562 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ C2×C42×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#1992 | C2 | semidirect |
| 3. C23×#1959 | C2 | semidirect |
| 4. C2×C23×#330 | C2 | semidirect |
| 5. C2×C23×#329 | C2 | semidirect |
| 8. C23×#562 | C4 | semidirect |
| 97. #8508 | C23 | direct (N × H) |
| 131. #1992 | C2×C23 | semidirect |
| 132. #1959 | C2×C23 | semidirect |
| 133. C2×#330 | C2×C23 | semidirect |
| 134. C2×#329 | C2×C23 | semidirect |
| 156. #562 | C4×C23 | semidirect |
| 209. C23 | #8508 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C23×#562 | 2 |
| C23×#1992 | 2 |
| C23×#1959 | 2 |
| C2×C23×#330 | 2 |
| C2×C23×#329 | 2 |
| #8508 | 23 |