Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
234 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 82 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 | #459 |
| commutator, Frattini, cosocle | C4×C8 | C23×C23 |
| prime radical | C2×D8×C23 | D4 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C42×C23 ◁ C82×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C23×#1707 | C2 | semidirect |
| 5. C23×#1367 | C2 | semidirect |
| 6. C23×#1364 | C2 | semidirect |
| 7. C23×#1362 | C2 | semidirect |
| 70. #12422 | C23 | direct (N × H) |
| 95. #1707 | C2×C23 | semidirect |
| 97. #1367 | C2×C23 | semidirect |
| 98. #1364 | C2×C23 | semidirect |
| 99. #1362 | C2×C23 | semidirect |
| 153. C23 | #12422 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2224 | 2 |
| C23×#2208 | 2 |
| C23×#1707 | 2 |
| C8×D8×C23 | 2 |
| C23×#1367 | 2 |
| C23×#1364 | 2 |
| C23×#1362 | 2 |
| #12422 | 23 |