Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
190 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C23 | #1345 |
| commutator | C2×M16 | C2×C4×C23 |
| Frattini, cosocle | #423 | C22×C23 |
| prime radical | C23×#575 | C4 |
| LCS | G ▷ C2×M16 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C2×C4×C23 ◁ C22×C4×C23 ◁ C23×#423 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#1327 | C2 | semidirect |
| 3. C23×#1307 | C2 | semidirect |
| 53. #7415 | C23 | direct (N × H) |
| 77. #1327 | C2×C23 | semidirect |
| 78. #1307 | C2×C23 | semidirect |
| 118. C23 | #7415 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2050 | 2 |
| C23×#1327 | 2 |
| C23×#1307 | 2 |
| #7415 | 23 |