Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
1556 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 1556 conjugacy classes of subgroups — too many to draw. Only its 142 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 | B(4,𝔽2) |
| commutator | C2×D4 | C22×C4×C23 |
| Frattini, cosocle | C22×D4 | C23×C23 |
| prime radical | C2×D42×C23 | C2 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C23×C23 ◁ C22×D4×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C23×#353 | C2 | semidirect |
| 3. C2×C23×AΣL(1,𝔽16) | C2 | semidirect |
| 4. C23×#1889 | C2 | semidirect |
| 5. C23×#1887 | C2 | semidirect |
| 9. D42×C23 | C4 | semidirect |
| 14. C23×#518 | C22 | semidirect |
| 17. C2×C23×#100 | C22 | semidirect |
| 18. C2×C23×#99 | C22 | semidirect |
| 74. C24×C23 | C22⋊C4 | semidirect |
| 93. C2×D4×C23 | C22⋊C4 | semidirect |
| 118. C22⋊C4×C23 | C22⋊C4 | semidirect |
| 121. C42×C23 | C22⋊C4 | semidirect |
| 122. #12759 | C23 | direct (N × H) |
| 175. C2×#353 | C2×C23 | semidirect |
| 176. C2×AΣL(1,𝔽16) | C2×C23 | semidirect |
| 177. #1889 | C2×C23 | semidirect |
| 178. #1887 | C2×C23 | semidirect |
| 211. D42 | C4×C23 | semidirect |
| 216. #518 | C22×C23 | semidirect |
| 219. C2×#100 | C22×C23 | semidirect |
| 220. C2×#99 | C22×C23 | semidirect |
| 274. C23 | #12759 | direct (N × H) |
| 285. C24 | C22⋊C4×C23 | semidirect |
| 304. C2×D4 | C22⋊C4×C23 | semidirect |
| 329. C22⋊C4 | C22⋊C4×C23 | semidirect |
| 332. C42 | C22⋊C4×C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D42×C23 | 2 |
| C2×C23×#353 | 2 |
| C2×C23×AΣL(1,𝔽16) | 2 |
| C23×#1889 | 2 |
| C23×#1887 | 2 |
| #12759 | 23 |