Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
366 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 78 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 | #1619 |
| commutator, Frattini, cosocle | C4×C8 | C23×C23 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C2×C4×C23 ◁ C4×C8×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#3293 | C2 | semidirect |
| 2. C23×#2213 | C2 | semidirect |
| 3. C23×#1709 | C2 | semidirect |
| 4. C23×#1358 | C2 | semidirect |
| 5. C23×#1335 | C2 | semidirect |
| 61. #12311 | C23 | direct (N × H) |
| 80. #3293 | C2×C23 | semidirect |
| 81. #2213 | C2×C23 | semidirect |
| 82. #1709 | C2×C23 | semidirect |
| 83. #1358 | C2×C23 | semidirect |
| 84. #1335 | C2×C23 | semidirect |
| 128. C23 | #12311 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3293 | 2 |
| C23×#2213 | 2 |
| C23×#1709 | 2 |
| C23×#1358 | 2 |
| C23×#1335 | 2 |
| #12311 | 23 |