Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
170 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 66 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 | #2233 |
| commutator, Frattini, cosocle | C2×C16 | C23×C23 |
| prime radical | C23×#2218 | C2 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C2×C4×C23 ◁ C22×C8×C23 ◁ C2×C23×M32 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#2161 | C2 | semidirect |
| 3. C23×#1426 | C2 | semidirect |
| 4. C23×#1419 | C2 | semidirect |
| 5. C23×#1400 | C2 | semidirect |
| 44. #13717 | C23 | direct (N × H) |
| 60. #2161 | C2×C23 | semidirect |
| 61. #1426 | C2×C23 | semidirect |
| 62. #1419 | C2×C23 | semidirect |
| 63. #1400 | C2×C23 | semidirect |
| 100. C23 | #13717 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2218 | 2 |
| C23×#2161 | 2 |
| C23×#1426 | 2 |
| C23×#1419 | 2 |
| C23×#1400 | 2 |
| #13717 | 23 |