Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
390 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | C2×#102 |
| commutator | C2×C8 | C22×C4×C23 |
| Frattini, cosocle | C22×C8 | C23×C23 |
| prime radical | C23×#3169 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C2×C42×C23 ◁ C2×C4×C8×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#2163 | C2 | semidirect |
| 3. C4×C23×#106 | C2 | semidirect |
| 4. C23×#1347 | C2 | semidirect |
| 6. C23×#500 | C4 | semidirect |
| 7. C23×#493 | C4 | semidirect |
| 12. C4×D8×C23 | C4 | semidirect |
| 77. #11744 | C23 | direct (N × H) |
| 106. #2163 | C2×C23 | semidirect |
| 107. C4×#106 | C2×C23 | semidirect |
| 108. #1347 | C2×C23 | semidirect |
| 126. #500 | C4×C23 | semidirect |
| 127. #493 | C4×C23 | semidirect |
| 132. C4×D8 | C4×C23 | semidirect |
| 171. C23 | #11744 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3169 | 2 |
| C23×#2163 | 2 |
| C4×C23×#106 | 2 |
| C23×#1347 | 2 |
| #11744 | 23 |