Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
576 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 118 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 | #386 |
| commutator | C42 | C22×C4×C23 |
| Frattini, cosocle | C2×C42 | C23×C23 |
| prime radical | C23×#3153 | 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×#2372 | C2 | semidirect |
| 3. C23×#1533 | C2 | semidirect |
| 4. C23×#1505 | C2 | semidirect |
| 5. C23×#1300 | C2 | semidirect |
| 10. C23×#497 | C4 | semidirect |
| 11. C23×#496 | C4 | semidirect |
| 36. C23×C4⋊Q8 | C2×C4 | semidirect |
| 37. C23×#127 | C2×C4 | semidirect |
| 54. C23×#97 | C2×C4 | semidirect |
| 105. #9441 | C23 | direct (N × H) |
| 147. #2372 | C2×C23 | semidirect |
| 148. #1533 | C2×C23 | semidirect |
| 149. #1505 | C2×C23 | semidirect |
| 150. #1300 | C2×C23 | semidirect |
| 174. #497 | C4×C23 | semidirect |
| 175. #496 | C4×C23 | semidirect |
| 206. C4⋊Q8 | C2×C4×C23 | semidirect |
| 207. #127 | C2×C4×C23 | semidirect |
| 224. #97 | C2×C4×C23 | semidirect |
| 230. C23 | #9441 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3153 | 2 |
| C23×#2372 | 2 |
| C23×#1533 | 2 |
| C23×#1505 | 2 |
| C23×#1300 | 2 |
| #9441 | 23 |