Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
482 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 90 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 | C2×AΣL(1,𝔽16) |
| commutator | C2×Q8 | C22×C4×C23 |
| Frattini, cosocle | #124 | C23×C23 |
| prime radical | C23×#3018 | C2 |
| LCS | G ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C2×C4×C23 ◁ C22×C4×C23 ◁ C23×#532 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#2126 | C2 | semidirect |
| 3. C23×#1536 | C2 | semidirect |
| 4. C23×#1404 | C2 | semidirect |
| 5. C23×#585 | C4 | semidirect |
| 8. C23×#456 | C4 | semidirect |
| 14. C23×#413 | C4 | semidirect |
| 16. C23×#354 | C22 | semidirect |
| 19. C23×#329 | C22 | semidirect |
| 106. #13570 | C23 | direct (N × H) |
| 150. #2126 | C2×C23 | semidirect |
| 151. #1536 | C2×C23 | semidirect |
| 152. #1404 | C2×C23 | semidirect |
| 172. #585 | C4×C23 | semidirect |
| 175. #456 | C4×C23 | semidirect |
| 181. #413 | C4×C23 | semidirect |
| 183. #354 | C22×C23 | semidirect |
| 186. #329 | C22×C23 | semidirect |
| 226. C23 | #13570 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3018 | 2 |
| C23×#2126 | 2 |
| C23×#1536 | 2 |
| C23×#1404 | 2 |
| #13570 | 23 |