Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
936 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 936 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 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ C2×C23×#117 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#2619 | C2 | semidirect |
| 2. C23×#2073 | C2 | semidirect |
| 3. C23×#2011 | C2 | semidirect |
| 4. C23×#1999 | C2 | semidirect |
| 5. C23×#1818 | C2 | semidirect |
| 62. #32764 | C23 | direct (N × H) |
| 86. #2619 | C2×C23 | semidirect |
| 87. #2073 | C2×C23 | semidirect |
| 88. #2011 | C2×C23 | semidirect |
| 89. #1999 | C2×C23 | semidirect |
| 90. #1818 | C2×C23 | semidirect |
| 142. C23 | #32764 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2619 | 2 |
| C23×#2073 | 2 |
| C23×#2011 | 2 |
| C23×#1999 | 2 |
| C23×#1818 | 2 |
| #32764 | 23 |