Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
906 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 906 conjugacy classes of subgroups — too many to draw. Only its 206 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 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C23 |
| prime radical | C23×#2615 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ C22×#41×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#2616 | C2 | semidirect |
| 3. C23×#2077 | C2 | semidirect |
| 4. C23×#2035 | C2 | semidirect |
| 5. C23×#2034 | C2 | semidirect |
| 6. C23×#2000 | C2 | semidirect |
| 7. C23×#1780 | C2 | semidirect |
| 94. #32716 | C23 | direct (N × H) |
| 131. #2616 | C2×C23 | semidirect |
| 133. #2077 | C2×C23 | semidirect |
| 134. #2035 | C2×C23 | semidirect |
| 135. #2034 | C2×C23 | semidirect |
| 136. #2000 | C2×C23 | semidirect |
| 137. #1780 | C2×C23 | semidirect |
| 208. C23 | #32716 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2616 | 2 |
| C23×#2615 | 2 |
| C23×#2077 | 2 |
| C23×#2035 | 2 |
| C23×#2034 | 2 |
| C23×#2000 | 2 |
| C23×#1780 | 2 |
| #32716 | 23 |