Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
298 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 298 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 | C22×C23 | C2×D16 |
| commutator, Frattini, cosocle | C2×C16 | C23×C23 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×C4×C23 ◁ C22×C8×C23 ◁ C22×C16×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C23×#508 | C2 | semidirect |
| 2. C2×C23×SD64 | C2 | semidirect |
| 3. C2×C23×D32 | C2 | semidirect |
| 4. C23×#2215 | C2 | semidirect |
| 5. C23×#1416 | C2 | semidirect |
| 6. C23×#1415 | C2 | semidirect |
| 7. C23×C22⋊C32 | C2 | semidirect |
| 33. C23×Q32 | D4 | semidirect |
| 38. C23×D16 | D4 | semidirect |
| 72. #13663 | C23 | direct (N × H) |
| 94. C2×#508 | C2×C23 | semidirect |
| 95. C2×SD64 | C2×C23 | semidirect |
| 96. C2×D32 | C2×C23 | semidirect |
| 97. #2215 | C2×C23 | semidirect |
| 98. #1416 | C2×C23 | semidirect |
| 99. #1415 | C2×C23 | semidirect |
| 100. C22⋊C32 | C2×C23 | semidirect |
| 147. Q32 | D4×C23 | semidirect |
| 152. D16 | D4×C23 | semidirect |
| 161. C23 | #13663 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C23×#508 | 2 |
| C2×C23×SD64 | 2 |
| C2×C23×D32 | 2 |
| C23×#2215 | 2 |
| C23×#1416 | 2 |
| C23×#1415 | 2 |
| C23×C22⋊C32 | 2 |
| #13663 | 23 |