Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
196 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 70 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 | #1677 |
| commutator, Frattini, cosocle | C4×C8 | C23×C23 |
| prime radical | C23×#2213 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C2×C4×C23 ◁ C4×C8×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#2244 | C2 | semidirect |
| 2. C23×#2231 | C2 | semidirect |
| 4. C23×#2171 | C2 | semidirect |
| 5. C23×#1369 | C2 | semidirect |
| 6. C23×#1366 | C2 | semidirect |
| 7. C23×#1357 | C2 | semidirect |
| 66. #12465 | C23 | direct (N × H) |
| 83. #2244 | C2×C23 | semidirect |
| 84. #2231 | C2×C23 | semidirect |
| 86. #2171 | C2×C23 | semidirect |
| 87. #1369 | C2×C23 | semidirect |
| 88. #1366 | C2×C23 | semidirect |
| 89. #1357 | C2×C23 | semidirect |
| 138. C23 | #12465 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2244 | 2 |
| C23×#2231 | 2 |
| C23×#2213 | 2 |
| C23×#2171 | 2 |
| C23×#1369 | 2 |
| C23×#1366 | 2 |
| C23×#1357 | 2 |
| #12465 | 23 |