Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
906 conjugacy classes of subgroups; only the 278 normal subgroups are shown.
This group has 906 conjugacy classes of subgroups — too many to draw. Only its 278 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C23 | #127 |
| commutator, Frattini, cosocle | C42 | C24×C23 |
| socle | C22×C23 | C2×#127 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C23 ◁ C2×C42×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#3169 | C2 | semidirect |
| 2. C23×#3147 | C2 | semidirect |
| 3. C23×#1722 | C2 | semidirect |
| 4. C23×#1721 | C2 | semidirect |
| 5. C2×C23×#322 | C2 | semidirect |
| 53. C2×C8×C23 | D8 | semidirect |
| 61. #19616 | C23 | direct (N × H) |
| 78. #3169 | C2×C23 | semidirect |
| 79. #3147 | C2×C23 | semidirect |
| 80. #1722 | C2×C23 | semidirect |
| 81. #1721 | C2×C23 | semidirect |
| 82. C2×#322 | C2×C23 | semidirect |
| 131. C23 | #19616 | direct (N × H) |
| 145. C2×C8 | D8×C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3169 | 2 |
| C23×#3147 | 2 |
| C23×#1722 | 2 |
| C23×#1721 | 2 |
| C2×C23×#322 | 2 |
| #19616 | 23 |