Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
472 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 202 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 | C22×D16 |
| commutator, Frattini, cosocle | C16 | C24×C23 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ #41×C23 ◁ C23×#131 ◁ C23×#504 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#3415 | C2 | semidirect |
| 2. C23×#2263 | C2 | semidirect |
| 3. C23×#2262 | C2 | semidirect |
| 4. C2×C23×D32 | C2 | semidirect |
| 5. C23×#2258 | C2 | semidirect |
| 8. C23×#508 | C22 | semidirect |
| 9. C2×C23×D16 | C22 | semidirect |
| 11. C23×Q64 | C22 | semidirect |
| 12. C23×SD64 | C22 | semidirect |
| 13. C23×D32 | C22 | semidirect |
| 14. C23×D32 | C22 | semidirect |
| 15. C23×M64 | C22 | semidirect |
| 16. C2×C23×C32 | C22 | semidirect |
| 43. #33982 | C23 | direct (N × H) |
| 55. #3415 | C2×C23 | semidirect |
| 56. #2263 | C2×C23 | semidirect |
| 57. #2262 | C2×C23 | semidirect |
| 58. C2×D32 | C2×C23 | semidirect |
| 59. #2258 | C2×C23 | semidirect |
| 68. #508 | C22×C23 | semidirect |
| 69. C2×D16 | C22×C23 | semidirect |
| 71. Q64 | C22×C23 | semidirect |
| 72. SD64 | C22×C23 | semidirect |
| 73. D32 | C22×C23 | semidirect |
| 74. D32 | C22×C23 | semidirect |
| 75. M64 | C22×C23 | semidirect |
| 76. C2×C32 | C22×C23 | semidirect |
| 93. C23 | #33982 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3415 | 2 |
| C23×#2263 | 2 |
| C23×#2262 | 2 |
| C2×C23×D32 | 2 |
| C23×#2258 | 2 |
| #33982 | 23 |