Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
734 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 734 conjugacy classes of subgroups — too many to draw. Only its 122 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 | C2×C42 | C23×C23 |
| socle | C22×C23 | #392 |
| LCS | G ▷ C2×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×#3100 | C2 | semidirect |
| 2. C23×#2397 | C2 | semidirect |
| 3. C23×#1963 | C2 | semidirect |
| 4. C23×#1486 | C2 | semidirect |
| 5. C23×#1274 | C2 | semidirect |
| 27. C23×C4⋊Q8 | D4 | semidirect |
| 28. C23×#127 | D4 | semidirect |
| 51. C4×C8×C23 | D4 | semidirect |
| 87. C42×C23 | D8 | semidirect |
| 91. #10012 | C23 | direct (N × H) |
| 127. #3100 | C2×C23 | semidirect |
| 128. #2397 | C2×C23 | semidirect |
| 129. #1963 | C2×C23 | semidirect |
| 130. #1486 | C2×C23 | semidirect |
| 131. #1274 | C2×C23 | semidirect |
| 176. C4⋊Q8 | D4×C23 | semidirect |
| 177. #127 | D4×C23 | semidirect |
| 200. C4×C8 | D4×C23 | semidirect |
| 202. C23 | #10012 | direct (N × H) |
| 237. C42 | D8×C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3100 | 2 |
| C23×#2397 | 2 |
| C23×#1963 | 2 |
| C23×#1486 | 2 |
| C23×#1274 | 2 |
| #10012 | 23 |