Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
384 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 384 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×#3291 | C2 | semidirect |
| 2. C23×#2213 | C2 | semidirect |
| 3. C23×#1721 | C2 | semidirect |
| 4. C23×#1359 | C2 | semidirect |
| 5. C23×#1336 | C2 | semidirect |
| 9. C23×#493 | C22 | semidirect |
| 16. C23×#364 | C22 | semidirect |
| 18. C23×#322 | C22 | semidirect |
| 59. Q16×C23 | D8 | semidirect |
| 69. D8×C23 | D8 | semidirect |
| 78. #12314 | C23 | direct (N × H) |
| 104. #3291 | C2×C23 | semidirect |
| 105. #2213 | C2×C23 | semidirect |
| 106. #1721 | C2×C23 | semidirect |
| 107. #1359 | C2×C23 | semidirect |
| 108. #1336 | C2×C23 | semidirect |
| 124. #493 | C22×C23 | semidirect |
| 131. #364 | C22×C23 | semidirect |
| 133. #322 | C22×C23 | semidirect |
| 165. C23 | #12314 | direct (N × H) |
| 180. Q16 | D8×C23 | semidirect |
| 190. D8 | D8×C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3291 | 2 |
| C23×#2213 | 2 |
| C23×#1721 | 2 |
| C23×#1359 | 2 |
| C23×#1336 | 2 |
| #12314 | 23 |