Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
458 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C23 | #120 |
| commutator | C22×C4 | C22×C4×C23 |
| Frattini, cosocle | C23×C4 | C23×C23 |
| socle | C22×C23 | #385 |
| prime radical | C22×D4×C23 | Q8 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C23 ◁ C23×C4×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C23×#1855 | C2 | semidirect |
| 5. C23×#1298 | C2 | semidirect |
| 90. #8860 | C23 | direct (N × H) |
| 118. C2×C4×C23 | #108 | semidirect |
| 129. #1855 | C2×C23 | semidirect |
| 131. #1298 | C2×C23 | semidirect |
| 205. C23 | #8860 | direct (N × H) |
| 273. C2×C4 | C23×#108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2975 | 2 |
| C23×#1870 | 2 |
| C23×#1855 | 2 |
| C23×#1459 | 2 |
| C23×#1298 | 2 |
| #8860 | 23 |