Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
518 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 106 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, Frattini, cosocle | C2×C42 | C23×C23 |
| prime radical | C23×#2819 | C2 |
| LCS | G ▷ C2×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×#1959 | C2 | semidirect |
| 3. C23×#1836 | C2 | semidirect |
| 4. C2×C23×#329 | C2 | semidirect |
| 5. C23×#1295 | C2 | semidirect |
| 40. C23×#97 | D4 | semidirect |
| 79. #10425 | C23 | direct (N × H) |
| 112. #1959 | C2×C23 | semidirect |
| 113. #1836 | C2×C23 | semidirect |
| 114. C2×#329 | C2×C23 | semidirect |
| 115. #1295 | C2×C23 | semidirect |
| 175. #97 | D4×C23 | semidirect |
| 178. C23 | #10425 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2819 | 2 |
| C23×#1959 | 2 |
| C23×#1836 | 2 |
| C2×C23×#329 | 2 |
| C23×#1295 | 2 |
| #10425 | 23 |