Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
252 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C23 | C2×D4 |
| commutator | C4 | C22×C16×C23 |
| Frattini, cosocle | C4×C8 | C23×C23 |
| socle | C22×C23 | C8×D4 |
| prime radical | C2×D8×C23 | C8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C23 ◁ C4×C16×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D4×C16×C23 | C2 | semidirect |
| 3. C23×#1367 | C2 | semidirect |
| 4. C23×D4⋊C16 | C2 | semidirect |
| 5. C23×#1312 | C2 | semidirect |
| 32. D8×C23 | C16 | semidirect |
| 47. #12062 | C23 | direct (N × H) |
| 50. D4×C23 | C2×C16 | semidirect |
| 61. C8×C23 | C2×C16 | semidirect |
| 63. D4×C16 | C2×C23 | semidirect |
| 65. #1367 | C2×C23 | semidirect |
| 66. D4⋊C16 | C2×C23 | semidirect |
| 67. #1312 | C2×C23 | semidirect |
| 106. C23 | #12062 | direct (N × H) |
| 109. D8 | C16×C23 | semidirect |
| 126. D4 | C2×C16×C23 | semidirect |
| 137. C8 | C2×C16×C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×C16×C23 | 2 |
| C8×D8×C23 | 2 |
| C23×#1367 | 2 |
| C23×D4⋊C16 | 2 |
| C23×#1312 | 2 |
| #12062 | 23 |