Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
648 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 138 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 | #379 |
| commutator | C42 | C22×C4×C23 |
| Frattini, cosocle | C2×C42 | C23×C23 |
| prime radical | C23×#3568 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C2×C42×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#1521 | C2 | semidirect |
| 3. C23×#1482 | C2 | semidirect |
| 4. C23×#563 | C4 | semidirect |
| 5. C23×H(3,𝔽4) | C4 | semidirect |
| 11. C23×#431 | C22 | semidirect |
| 12. C23×#383 | C22 | semidirect |
| 85. #8514 | C23 | direct (N × H) |
| 105. #1521 | C2×C23 | semidirect |
| 106. #1482 | C2×C23 | semidirect |
| 119. #563 | C4×C23 | semidirect |
| 120. H(3,𝔽4) | C4×C23 | semidirect |
| 126. #431 | C22×C23 | semidirect |
| 127. #383 | C22×C23 | semidirect |
| 170. C23 | #8514 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3568 | 2 |
| C23×#1521 | 2 |
| C23×#1482 | 2 |
| #8514 | 23 |